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Propose autograph order

it is the lasalle education complete maths autograph webinar course part of a four-part series last week we did the shape course which is available on the LaSalle ed a YouTube channel where you can watch and listen and hopefully work your way through the tasks that we've completed all the resources are available on the LaSalle education a complete math website wwlp.com this week we're looking at session 2 where we're going to look at some line tests graphs of the form x equals a and y equals b we're going to look at using the constant controller for y equals MX plus C some solving equations completing the square infant inverse functions trigonometric graphs and so much more hopefully you'll find the session useful we've emailed out some how-to guides and some tasks which hopefully you've got but we'll try and drop them into the chat as and when we use them and this week your co-hosts again myself Robert Smith and Douglas Butler you can follow autograph maths on Twitter with at autograph maths and the solid occation atlas l-e-d doug and i look forward to your feedback and comments as well as any screenshots or little video clips that you might want to share from the creations of it nota Graff and Doug if you'd like to kick us off with our first task it'd be much appreciated and I'll take to answering questions and comments in the chat well good morning everybody and for those of you who were not here last week this is certainly a new experience for you I've had one go at this so far already and it's been good fun when you first launch autograph you get this welcome page which possibly does suggest that it really is only useful for teaching a level maybe we should put some extra scenes in here but anyway there are lots of opportunities for using autograph and the ages 11 to 16 so that's what we're concentrating on today and let's let's start away I'm just going to open up a file left over from last week who didn't quite get round to it and it's quite a nice one on triangles and tests for parallels and so on so what I've got here I've just got a couple of line segments and if you double click on each when you see that I've locked these three points so I can move this one around and the challenge is to move it around until you find that one line segment is perpendicular to the other you could just sort of guess but it'd be much better if you actually worked it out there we are that is three long and one down so one long and three up will be perpendicular also by the way they're equal so you might think if this is very useful but you know as a teaching tool maybe two screens next to each other would be quite good one with the original and one with a blank screen so you can see how it all works I'll do that in a second just to show the other thing we wants to look at was triangles and properties thereof so I'm going to open up a new page and whichever page you have highlighted will when you do window windows and we're going to press the control key to select two windows I want page six and I want the triangle one and we want to tile vertically now you can see that the empty page is the one that I have highlighted so I can move this across and move this one across notice that if I hold down the mouse and just let it go it becomes the drag or if you're not sure about that just press the drag like that we've also got the key down here which is for plotting a quote for a listing equations but I'm just going to take that away okay one thing that is new in autograph five is the extension to the point mode so this is this is putting points on and you'll notice we're in this standard level and if you're not sure about that it should say one and not point one here if it says pi/4 radians then you're in the wrong mode because we do want to have everybody on the same one so if we do view preferences and just switch across from advanced to standard then all the same standard has no calculus and has no radians just a simpler interface and also putting points on that only goes to horrible to integer values but you can always put point 1 if you want to be in Gore detail that is a select mode which you should always return to in order to do anything useful so drag select is a way of selecting points and right click delete so if I extend this you'll see that you can normally put points on you can put intersection points which will use quite a bit today and you can use line segments or vectors or circles line segments is what you want and we want to put a line segment down here I'm on point one I'm in to do one so select again two so that it locks into interval is what I wanted and to another line segment say like that now at the moment they're clearly not parallel or perpendicular or anything or equal they're equal in fact that the test to do it is to select the two line segments and right click it's a line operation again if you are new to autocar five you'll be surprised to see these submenus here but it's just a very neat way of getting a lot more options so you want the parallel test and you also want the Equality test and you can see that as you move this around it becomes parallel and equal and oh sorry that's that's parallel down there so it's quite a nice little exercise to have a look at this if you want to know how to lock a point double click and just do lock one or both coordinates we've got an exercise that you don't want people to mess it let's mess it up and that's quite a good one to do so I think we probably pause at this time give you a chance to you may want to practice this this idea of having two screens open but certainly the idea of using the segment mode that's this one here to create segments at different places and then explore remember to do the tests you need to do select the two segments right click line parallel test or equality test depending on which you want or both okay we have to propose now I'll give you a chance to practice them how to guides and the tasks I've shared the lines test document into the chat so if you haven't got that to hang you can pick it up from there Doug I think some people were asking how to do the split window mode so if you just want to quickly show them the window menu at the top yep certainly if page six let's just have a new page supposing this is the page anyone you want six and seven and you want seven to be on the left and you want the triangle to be on the right go to the windows menu right down the bottom it says windows and as long as the one you want on the left is highlighted then you select that and you have to press ctrl just as you do in any other environment to do a knowledge non-fiction so not next to each other and then vertically or horizontally vertically it's the sensible one to do and then click OK and there it is there's seven on the left and this on the right Jill's asking how do you do the test after selecting boats their lines Durga's with a right-click jill and you select both lines using select mode select mode click both lines right click lied and parallel test and the Equality test you can lock the point by double-clicking on the points it'll launch the enter coordinates box and you can just tick the lock option I think the how2guide locks three of the points and you can move the other point around it might be useful to show how to hide the axes there as well Doug for those that might want to hide the axes it's just a single click up here yeah and to get rid of this right click don't show the key if you regret that decision and there's no option to put it back again it's in the axes menu choking and remember we are an equal aspect mode which is very important because if you're testing whether something's perpendicular to something else it'll look very strange if you're not in equal aspect mode because you'll find something that appears to be not at 90 degrees potentially as marked as such zoom so a good way to miss that up and if you want to zoom that triangle and make it a different shape altogether you can see what you got here that is not right what is it is it right angle mathematically but visually it's not so equal aspect we'll sort out the x scales so that it is indeed correct and then you can use grab mode to recenter back to the center of the screen indeed perfect so hopefully you're able to follow along with that if we give you another minute and then we'll show is the Equality test using the triangle and calculating the area and don't quit questions someone's asking if they can close the welcome page if you click the welcome page on the far right-hand side there should be a little X that you can click anywhere close that I'm not sure that that works you might have to consult with mark on that one it's a very nice page and it's just sort of likes being there doesn't get in the way once you've started something else it's just in the background with answers a question mark one thing I didn't mention was how to display the labels associated with a point and also just to change the shape of the point so if you've got this point selected right click Edit draw options very very useful this for any object you can change its appearance in particularly with points if you want this point to look different to the others which are locked it's just down here that it starts off as a circle and I've chosen diamond and normally it's 7 but if you bump it up to 11 or 12 you get a nice big one which looks very different also with that selected right-click you can edit its label or if the labels not there at all like this one for example you can show the label now the label will just be a capital letter but on its own but you can edit the label so right click edit the label and you have these choices here you can call it what you like you can show its value and you can fit it so it's all sort it up all the ticks on the right place move this around a bit but it is attached to that point because if it if the point moves the label moves with it don't one last question someone's asking there where the parallel test is again so if you just select both lines that both lines black right click line parallel test it's got double arrows because we've done it before yes now what you got here is is I think something the fact that the area of a triangle is 1/2 the base times the height is something you can prove very simply with lots of triangles and and even when it goes negative you're subtracting areas well it is nice I think to show it dynamically so what I've done here I've put a point here and I've put a horizontal line through that point so that that line is fixed and this is the point I'm moving along I've also created the midpoints and I've checked that they're parallel and I've done the closest point from the vertex down to the base so let's go over here and show how all that's done to right click don't show the key aha I'm still you see that that's that's white and that's brown that's the one that's actually occupied so if I do right click show key now click here to get my attention on this page and then right click don't show key okay I'm just going to drag this across here I'm going to put a point here because I want a horizontal line through that so a point and right click line horizontal line then back into point mode I'm going to put a point here and put a point on the line somewhere doesn't matter where and a point down here that's three points I'm selecting them although we need to a marquee select like this it only selects points does not select anything else like lines so I've got three points there and I'm going to group those into a shape and that shape you can move these around you can move these around to if you wish so this is a series of points if I select two of the points and this is how watercraft works you select and then right click point midpoint deselect always desolate before you start a new selection select select right click point midpoint now I need to go to the segment mode because I want to draw a segment from wait for the little white triangle to see doesn't know where to wear it where it's going to end up but if you end up here with the right triangle right in the middle of it it's quite happy and we want a line segment along here and now select the two line segments and right-click select the two segments I must have heard something else select R there's a point set there as well now look that's got it it was selecting these shapers at the same time so right click line parallel test then to do the perpendicular from here to here select the point select the line at the bottom the base and right click it's a point thing to show the closest point that's a little bit thin so I've selected that and and gently to go to edit drawer option because it's up here just make it a bit thicker it's better now how about measuring the area pretty simple diagram there so half the base times the height you can do it in your head but it's good to show that autograph is on your side here and can give you a hand let me introduce to those who weren't here last week the calculator very very useful because every object graph has attributes this triangle has a perimeter and it has an area so if I hover over it you can see that it's offering the calculator of the perimeter of the area so every two area it calls itself B because that's the label on this thing if we were showing labels and just put area equals with a couple of spaces click OK and that becomes a live box hang on I've got everything else selected there that's not good right so it stays at 6 whatever we do to this so see if you like to have a go at that remember the it started off as just three points that you can yes I'll just do it on this new triangle so you can see where it works so there's a line segment there and we want this point and this line segment and right click point closest point and that will drop a perpendicular as required Dan hopefully that answers your question how to get the closest point from the line segment for the height of the triangle always remember deselect by clicking nowhere before you start a new section and don't bang if you want to plot the midpoints on your new triangle so you select both points that you want the midpoint for just select select right click right click point midpoint hopefully that answers your question how to get one midpoint if you create the midpoint the other side point point right click point and midpoint the instructions are in the how to guide so you can refer to the document hopefully that'll explain how to create the triangle the books demonstrated or one similar always remember to go back to select and page they'd wants to know how you lock points Doug so if you just go to select mode and will click the point it will launch the Edit coordinates box and then you have the option in the checkbox to lock most coordinate points again it's in the how-to guide hopefully that's useful and if you've got any other questions feel free oh how to plot the line and from Josie and so if you just put a point on the page Josie so you can put a point there on the grid and then you right-click and in line mode you can create a horizontal and vertical mode their lines and creating the line segment that represents the height of the triangle you click the point and go to the line and right-click and in the point is the closest point option in the point closest point from the point menu remember if you want to the area of your triangle you just click the calculator select the triangle and you have the option there too perimetral the area we're going to choose the area we can put them before text we can type area equals to constructive I think if you pull it over this way and of course there you're talking about subtracting that area - this area same result cool and Matt Hein is asking can you attach labels so they move when the shape moves yes Matt and you can attach them to the point like the coordinate point there it's got the label attached to it but you can also have the labels not attached to the point don't might show you how you can attach to the point connected right edit label we don't want to call it f but we'd like to know what its value is we can do that and need to show it this space for some more text say if you want to and that will now change you can put it out of its in the way and Jen's asking how you lock the top point of the triangle to the horizontal line Doug yeah once the line is in place you see wait for the black arrow I remember it's it's locking onto whole number values because we're in the standard level and we're on that and then if you go back to select you can move it along and just one more time on calculate in the area again dope so click the calculator the calculator will launch the calculation box you click on the object when you want to calculate something for so for example the shape you want the area or the perimeter you click the shape that will show you the options available we've got perimeter in area and then we can fill in the before text or the after text if you want to calculate the height of that perpendicular line you should be able to calculate the length of the line Doug yes indeed it's it's an object like everything else so open the calculator and click on it and it's giving you the distance that's the one which is three hopefully that answers your question Matt and then you can move that text box to where it needs to be okay so dog if you want to launch the keyboard from the top menu if you click view and then keyboard that will launch the autograph keyboard so then when we're in the text mode you can then edit the superscript for the two four centimeter squared so double click on your high labeled ugh I didn't catch that double make the height label I am in the after-tax do you want to put centimeter squared so we're going to not for height but I'll just pretend so this area okay centimeters and then squared yeah I know so we've got subscripts as well here which have their place and let's raise to the power of n and this is really useful if you're using as I am I've got a keeper mouse pad here but I think it's very important that if you're doing something and it involves a bit of keyboard work and your students can't be sure what on earth you're doing where's this way you can see exactly what you're doing so you want to delete something press Delete and there it is or if you want to arrow keys just moving a point around with the arrow keys is very important and if you press control it doesn't intense your shift control it does it in hundredths and carats just asking how you get the arrow option don't know where the hair three points have been clipped to a shape so can either show how to group to a shape from last week okay yep put three points and one on there one down here select select them all as a marquee select remember the only selects points and right-click group to shape hi agrestic Garin you can calculate the area just by clicking calculator click the triangle and show the area doc I think it's about time we moved on to look at our x equals and y equals graphs and Lu come to y equals MX plus C I think so what we've got here is it's a nice visual look at the classic straight line y equals MX plus C and trying to explore what the M and the C stand for and to sort of get ready for that just to be sure they're understanding there the sense of coordinates and they put a blank page on like we did before and have those two selected so I've example to get this line here this is a it's an x equals a lot of students have trouble with this because it appears to be something to do with why but in fact why is is the same all the way along it so it's an x value if you enter an equation it's right click enter equation and if you do x equals a what you get you can edit the constants at this point but the all the constants in logic I'll start off at one so if a is 1 then it's going to draw along here now that was a bit sudden I would much rather Institute over brought it to the slope lot and it's no point is fantastic I'm not sure we want it quite as fast as that but this is a reap lot and off you go so you can see you've got plenty of time to sort of pause and think where is it going to go next this particular case is fairly straightforward that was x equals a and if you do actually click there y equals B again that's going to be this way now again it's not totally obvious why it should be that way around but if you think about it for all values of X Y is B so then you might set some targets and say right let's go down here what a and B going to be to bring those two lines go through that point so that's the first exercise that to look at and then to have a look at our old friend y equals MX plus C now M&C will both be one to start with so where's it going to go have a billion think what did actually go through there now the first time we've used the constant controller and in this session console polar is one of autographs masterpieces I think because you can not only change the value but you can also change the step now that was changing a because that you've got ABC in there modes of the whole if you want to take a down to here for example there it goes maybe want to take B that's the way of changing a and B so that goes through that target now what about that what's going on with this function here so let's let's have a look at the intersection mode this is a good way of finding out where a particular function hits an axis you can do it down there as well since you get the little circle that you can create a point now that's that's a point mmm what I'd like to do now is do a unit gradient now what that does it goes one to the right and then then so far up to when it hits the function again now what I'm going to do now is increase the gradient m and see that that's what happens aha now the really nice thing about this console controller is that if you had a slider bar which all the other programs have got side it was things was around too quickly so it's really good I think to be able to go down so far and then reduce the step our left and right reduces the step by a factor of 10 so that's that's gonna go much better now something quite significant happens now and then what happens well your ex is still one your change in X but this is now negative two this is what we call a negative slope what about C what does that do well clearly when X is zero Y is equal to C so when X is zero Y is equal to C so C is 1 at the moment but if we make C bigger and the nice thing about having this triangle here you can increase C and it all moves up one but without this of course you could just as easily describe it as moving to the left so I think it's quite important that that distinction is made so that's covered most things but the quite a nice task I think there is to put a couple of points on and let's do this that's here let's go back to point mode but it's a point here and a point here so in there and let's find a straight line that goes through those points first thing you want to do of course it's work out its gradient and then playing around with M and C until it goes through that point that I leave you as a little exercise how we go this still there Rob yeah still there we're going to have a look at the tasks in the y equals and the x equals to get the gradient triangle Doug can you just show how you got the grade any point on a function doesn't matter where it is you can ask for a line option of the unit gradient so that simply matches one to the right and then however far up one to the right then however far up as you change things it's this increase the gradient you can see that it is that step now is point one which is why it's going in small bits and it goes negative obviously with a straight line it's gonna be a lot more interesting when you've got this happening on a curve and the constant controller you can get from the toolbar it's the K with the two arrows left and right or you can click view constant controller again all the instructions in the how-to guides with the tasks and questions that you can use as well and Oh Doug if you can click the calculator and in the box if you can just put N and then in the before text M equals and then if you click the calculator and put C and C equals or y intercept equals that's one way that you can display the values of m and C so what do we got here the gradient is too long and one down okay so the change in Y over the change in X minus 1/2 so put that in so we change em to minus 4.5 and just check that is parallel to that so all I got to do now is change C reduce the step come down a bit bingo and a quick question there Doug and is it possible to display the height of the gradient triangle come here can't remember so look ah I thought it was but God is an odd because another thing to look at which is the text box sometimes carries information but no it only gives the gradient you could construct your own gradient triangle and calculate it Rob so hopefully that answers your question we'll give you some time to have a go at the tasks in the document don't you want to show the tasks in the file and number 2 graphs and wipe their X + C and the you don't need to select the line to get the constant controller to display you just deselect by clicking anywhere go in view constant controller and question about locking the textbox so they move when you change the line is that possible dick after thinking about the constant here because this grade because that's one then the value of the gradient is automatically the distance right here so it's the same thing that is that - not 0.5 any other test document Doug yes and number ooh x equals and you'll see that all the instructions on how to do this task go in there and if you get to the end you'll find some graphs that you can construct yourself using parables and pageants asking how you were animated the line being drawn using slope hot dog so if you want to just quickly show how to turn slow plot on by clicking the green icon in the toolbar yep you can either put it on here what I was doing or you can put it on here it's off now and it's on and if you want to go back to the equation entry box double-click on this you're back here again and just press ok but this time it's going to go slowly so you could you could pause it now and ask is it going to come from up here or down here I'm hoping it's going to end up going through those points snow pot speed is up here a little pull up pull to the right or left and thanks Nick yes it's documents to a and to be that we're looking at at the moment so if you've got any questions about the tasking there is drop them into the chat and hopefully the instructions are there that you can follow along with all the options of how to turn on the constant controller and which menu to click to enter the equations and the like and thanks mark for sharing the job links to the files for this week so I'm going to put on and we just got a couple of quick questions don't you label the y-intercept so we're going to go to the intercept point it's the intercept mode wait for the little circle and though it is and depends what you want to say to it so let's right-click edit the label and you can call it what you like intersection follow-up question to that mark is asking how do you display the results box to the right hand side we can do that from the axes it's in the review view although all the things you want to show are in here and results books what the results box is is simply a collection of text files of things objects that we've created and their results it's just there for you to do whatever you like to you there's text you can select right click copy put it into a Word file also on the key to the right hand side dog oh very rarely use that but you said you can this is the key at the bottom and this is the key at the right hand side lines as well that's true yes it can go all the way down yeah can you make the key narrow the dough can you extend your screen back out and have the key box smaller no it's the way it's setup it's a square from axes and view rather than from there oh yes you can have more down here that's what I mean yes I haven't told people that if you double-click on any axis you open up the Edit axes menu and one of the options is to say how many entrance you want in the key so if we bum this up to six metal enter oh yeah but if you go and access dug yep Eddy taxis options key right and a picture five entries or six entries and click OK that doesn't put it into square mode so you can have it a narrower key that way well there we go that answers your question mark how long have I been playing with autograph and I didn't know that should we go on to look at solving equations doc because there's quite a few tasks in there document number three and I think it'll be useful for people to have a bit of time to be able to play with they're solving equations there's some nice questions in there ah so it's a similar tennis linear equations we're looking at now that's correct yes now the form for the straight line y equals MX plus C's is one way introducing people to straight lines there's there's another form which is a little unusual because it's not x equals or y equals it's a bit of both so let's do enter equation now and let's do 2x minus 3y equals 6 so it's an unusual format as it's not y equals not X equal so it's both so click OK you've got the slope right answer pinch time to think about it and now you stop and the stop is really really useful so when x is 0 or whatever got Y y is going to be now this is where the pen is quite useful so I like to introduce you to the pen now it depends what you've got with you if you've got a mouse that's really helpful because you can click on this and you can draw a little circles with care if you've got a pen like I have you can be even more careful and so what do we got here but x is 0 Y is negative 2 so it's down here so definitely going to at that point then y is 0 X is 3 so it's going to go through here right so we're expecting it to appear from down there and to go through up like that that's the sort of chat you want to have before you plot anything that's the autograph way and it goes boom and of course if you've got that wrong that of there's plenty of learning there to be had as to why it was wrong and so on edit select all scribbles and delete so now we put on a second equation there's 2 X minus y equals 3 something like that that may not intersect well that's we'll see just you fast-forward very boring so let's change it to something a little less boring let's put a 3 in there that was available with it so let's look at solving the intersection even though we can see where it is dug and then we can look at some of the examples than the tasks that actually have the questions that they can have a go at themselves and solve using the intersection so you have there's two ways to look at this one way is to just literally zoom away and just zoom zoom zoom zoom zoom and what are we ending up with here it looks like that's eight but this is going to be some fractional value if you get in the model and zoom and you literally lose everything just press the red tick your contract you might want to do equal aspect as well now getting the computer to give you the answer because obviously you do it by algebra but it's good I think that the computer can do this for you and just wait for the little circle and then right-click you can edit the label and you can show the answer by showing it I think how to guide also does it by collecting both lines and solving the intersection don't look if you select both the lines as and these needn't be straight lines it could be curves or anything else but you can right click point solve intersection and whatever you select that and then the text box it tells you in a nice sort of format intersection equals now you might want to change the anchor as well Doug for the point just show how that works yep if you double click on the this this is a text box and you don't want it to anchor to the point you can then Park the text box somewhere over here you may want to do that or you can edit the minimum distance and it's away so it's yes like further away but still close to the point so double click and anchor but minimum make that thirty sort of maximum so to display the tasks and there's I think about ten questions that people can have a go at there's lots of different equations that people might want to use the keyboard and use the fraction elements on and this is number three hopefully the step by step instructions are there that will allow you to solve these but you can hopefully have a go at some of those to build your confidence with using solve intersection dude why didn't you have a go at demonstrating number one they're 2 X plus y is 18 and X minus 2 y is minus 1 so 2 X plus y equals 18 so enter equation 2x plus y equal 18 okay and slope will takes their part off now it's being a bit slow and then the other one is X minus 2 y equals minus 1 X minus 2 y is minus 1 and if you use the grab mode you can use the grab to bring that to the center and you can use the point mode and find the intersection the little slack will appear when the in sections there and then you can display the text box or anything able to display the intersection so the solution would be 7 for X and 4 for y hopefully you managed to create that one and there's some of the therapies have a go up we just want to build your confidence using autograph for solving equations and we'll spend three or four minutes just happen again and some of those tasks and hopefully you can have a go of those any questions drop them into the Jats if you want to know how to display the label or any of the other options feel free to drop it in the chat and we'll give it a go mrs. moles asking why the intersection is a square instead of a circle and when you get to the where the intersection is it turns to a circle and then when you use the select mode if you select the point right click and edit the label you'll see there that you've got the show label and enter to point and then that would be why the Anchor Point option would be greyed out as if it's a text box that's not attached to a point Ben if you wanted to display a mixed number in the equation if Doug has his keyboard on it can do equations enter equation and then he should be able to use the keyboard to do is five and a half fraction by clicking five and then a half symbol then you've also got the third option there I think entran is an improper fraction is probably a nice way to do that at the moment if you need a workaround as to how to enter a mixed number fraction or you can do it looks like we're about an hour into our session doke so maybe it's time to have a look at the next section hopefully if there are any questions you can drop those questions into the chat I know there are some tasks attached to the next section Doug so we want to maybe click to those okay what I thought I'd do is is push the next two on because there's some other things I want to cover if possible before the deadline the next thing is obviously straight lines we've had and things that curve through what first ones they come across are the quadratic curves and the king of wards of course is y equals x squared and just to xx give you an x squared and if slope right is still on then you could discuss where it's going to come and so on so how that gets transformed by various other numbers attached to the equation is very important so if you do y equals a X X where a is a number a will be one to start with so it's just going to plot straight on top of the other one but looking to see what happens to a as you change it let's have a look at the constant controller now and I'm going to press this button here which will make a two instead of one what's going to happen to the graph don't just do it and say look see if you can puzzle it out obviously when X is 1 x squared is 1 so if it a it's going to be 2 2 X Squared's going to be after that let's have a look and see Ready Steady Go yes down the bottom but a game with it with a slider bar things tend to happen far too quickly so what I've quite like to do is get down so far and then reduce the step slowly this is a good time to introduce you to the animation possibilities of the constant so if we have a look at the options here you can do a family plot of graphs with particular values or you can do a and animation up and down just animation up and down let's go from minus 3 to plus 3 in steps of point one that's pretty good click OK and then watch it do it so they should get the a really good a feeling of this that when you have a quadratic expression and if the sine of x squared is positive then it's this way up if it's negative it's that way up okay so we'll go back to manual and make it one again so what I want to do now is have a look at what happens if you do enter equation y equals brackets X - list of B but well still wanted squared squared is here now I'd like B to be 0 to start with so that you can get that in and that that means it's going to start off exactly where the other one was so there's no change but now if we change B which way is it going to go now if you look at this when x equals B that's when Y is equal to 0 therefore the value of B tells you where the vertex is going to be so if B becomes 1 the whole thing is going to shift to the right to here so that's going to be the origin at the vertex let's have a look and see if that is indeed the case yes again try to anticipate all the sort of thing before you press ok and as a general rule to have a look at this let's have a look at one that I've got here hmm now once you've understood what - a and B actually mean this is quite a good way of having a look at rearranging this equation as a perfect square and if you do so I'm suggesting that x squared minus 3x minus 1 which is the red one can be reformed as X minus a or squared plus B well I'm going to start off with a equals 0 and B equals zero and so it's just like that so what do I have to do to open up the console controller and just make sure that this graph ends up on top of this one so what is the translation that's going to make this happen so first of all I'm going to change B but what I quite like to do is have a look at here the intersect mode shows all sorts of things it shows you where that intersects the x-axis also shows you where the minimum is so in that I'm going to draw a vertical line I'm going to select the line and edit draw options and make it dotted that's better okay can I get this orange one to sit on top of the red one let's have a look first of all I'm going to change a now I'm not going to change because I want to move it to the right I mean a forgive me all right I'm going to move it to the right until such time that is is symmetrically placed over the other one now I'm going to change B which is going to move it down is it going to no it doesn't quite meet it this is where again a slider bar would totally fail I know I want to I want to reduce the step to 0.01 and there it goes and if I'm not sure I can always get the zoom and take a look yeah that's absolutely bang-on red tick will get us back to sanity and finally I'm going to put a point at the origin enter coordinates 0 0 and I'm going to create a vector on there of a B to really hammer home the idea that this is a translation vector a and B should take this point straight down to there so that's a visualization of what goes on in a very algebraic process of changing this into this telling it's probably not for you to have another play with the bottom of the document for B Duke has the task so if you want to scroll down to the bottom there you can see we've got some examples there if you'd have a go hopefully you can drop the questions into the chat and we'll do our best to assist you we're using this for completing the square I'll just drop that document again into the chat for those that haven't got access to it hopefully you're able to follow along I hope but if you've got any questions or comments drop them into the chat and hopefully you're having a good game at the example that Doug's provided there and following through the instructions in the how-to guide now you'll see that there are four parts to task one and hopefully you're able to use the constant controller to adjust the step accordingly to find the transformation don't Kate is saying that she's put a point at the turning point and made a vertical line but the line doesn't move when she changes the constant I would think that means that the point isn't connected to the intersection there Katie so good you want to just demonstrate to Katie how she might do that I'm just deleting the victor out of the way okay here is the the Virgin graph although let's just move it away somewhere else now one of the options in the intersect mode here it not only finds intersections with the axes or with other graphs it also finds its Max and min points so that is definitely a point that you can't move because it does it's life to that graph it won't move anywhere so there you select that and right click would align vertically to that deselect select the line right click Edit draw options make it dotted or whatever it's a construction line requesting Katie but you're doing really well so keep dropping those questions and comments into the chat and saying that when she enters her equation it doesn't appear and may I ask which equation you're into and just so we can there see what happens it might be that we need to zoom out in order to see it with the axes that we've got x squared minus 2x plus 16 big R 16s off the top isn't it so that that's almost certainly let's try in it something like that so we should go to use grab mode and we can slide or zoom out and then grab it certainly there hopefully that answered your question and you can use a zoom in and out on the left hand toolbar and Jill's asking how you draw the vertical line from the point again so if you create the point and right-click and in the line mode you've got a vertical line there Jill so you should be able to hopefully manage to create that vertical line and fill saying these got the points at the minimum and so when the point is at the minimum fill if you just click the point and right-click then you should be able to right click and create a vertical line if you created the turning point you might need to go and add an additional point on top of the turning point by clicking when the circle appears right click in choosing line and vertical line there hopefully that answers questions philatelic abut if you need further help there drop a comment into this chat and we'll do our best to help you before we're gonna have to move on I think yep we can't decide what I'm gonna do in the last quarter now I would stick with number five y equals x to the end yeah that's good one so new page once they've got being introduced to the quadratic function of course the next one is cubics and reciprocals and and so on so it's just an exponential function as well quite a tricky set of ideas to get across so let's enter an equation I like to put a white with X square because it's a sort of king of everything really and then if you do y equals x cubed but before you do so I think time to get pen out I've tried to find this with some quite senior students you know they haven't been visualizing their mathematics as much as they could so if I asked them to draw y equals x cubed on the same graph as y equals x squared you get all sorts of results from even quite talented mathematicians because I haven't really thought it through so you say write x squared is x times X but X cubed is x times x squared so it's going to be x times whatever it was when it was squared so for example when X is 1 obviously one cube is that the next is 0 it's there and when X is minus 1 it's there when X is 1/2 it's going to be 1/2 of what it was when it was cubed so it's there it's going to be 3/4 of what it was when it was squared and then it goes in because it gets sandwiched into the constants of the zero here then the same thing happens on the way out down here I have that sort of discussion before you then put into equation y equals x see I got on I should have had this way about on give me that's me plot then edit select all scribbles and delete what it's quite useful now is to convert this into not white because X to the power three but Y is X to the power of n now n of course is another constant and it'll start off with a value of one so if I press ok what's going to happen it's going to be the line y equals x at 45 degrees take slope odd off now but now the console controller kicks in console controller and in steps of one I'm gonna make n2 what we know about that 3 we've just been exploring what about 4 what about 5 what about 6 what about a hundred what's it going to do when it's is it going to be a right angle at that corner well it's going to have a look so it's got to get up to one one but it just takes a long time to get on with it red tic sorts out the scales equal aspect just in case so let's go back to it to reduce the step so increase the step to 10 rather and bring this down to 90 80 70 60 50 40 30 20 10 reduce the step 9 8 7 6 5 4 3 2 1 what's gonna happen next really good thing now if they've all got their own little drawing pads or whatever see if they can predict what's gonna happen what we're talking about here it is made of using technology that I've been really keen on all my life really a big screen in front of the kids and they've got some way of recording what their thoughts are and they can share it with you obviously a fully electronic system is great as well but that's fine this guy for most beautiful so the frame is zero-- of course it's going to be that then what happens when n is minus 1 try to do a table of values and this may be the first time they come across infinity who knows but there's so much to talk about to get before they get that shape and that is in the curriculum for the secondary course I don't think I'd have to go much further there's no reason why they shouldn't start doing I mean the inverse-square very important will television signals and all sorts of things so having a look at those is important I think we're going to have to push on because I want to show you the y equals two to the X tooth by vechs it's a very important function it's the doubling thing those have been watching the quiz program last night will they understand that doubling is a pretty important feature of mathematics and when it comes to monies from five hundred to a thousand a thousand to two thousand and so on it starts to get serious and that's the same happening here so make sure this web product is on because there's lots to talk about here the fraud actually gets anywhere and this is where the pin comes in again so when X is zero what's 2 to the power n ething to the power 0 is 1 2 to power 1 is 2 2 to the power minus 1 is going to be 1/2 2 to the power minus 2 is 1/4 yes are we go now if we zoom out of this you'll begin to see what an amazing function to survive X is it just goes to the moon and if you're talking about Who Wants to Be a Millionaire and that's what's happening up here the questions get pretty interesting red tick notice also that everything I've done is stored away in previous pages along here very useful to be able to look back at what you've been doing so what we're doing in this segment session was having a look at y equals x squared and then y equals x cubed y is raised to the fourth and so on that's minus 7 minus 6.4 0 that's a very important one 1 2 3 4 so it's just entered very simply as y equals x to the power of n in relation to y equals x squared and then we had a look at two to the X so have a little quick way on that but we are running short of time but just so you get a feel for how easy it is to enter these equations and with constants and consonant trailer to explore but I've dropped document fighting to the chat again it's available in the drop box talks with quite a bit about using their slow plots and you know to use the pause options there Doug and so hopefully people can have a go with that now we have got documents six seven eight and I think we're probably going to have to use at the beginning of next time or you can have a homework task to work through those the instructions are fairly straightforward to follow and you can always drop us comments to at autograph maths and at the cell ed hopefully it'll give you some extra practice to work through some of those examples and answer some of the questions with how you actually access those documents so I look forward to seeing those tweets that share that information and I know that you all appreciate getting homework I'm glad that you're finding the Reg tick default scales useful it is a lifesaver it does bring you back to the center so really useful don't question our are there any prohibited letters for using as constants yeah we treat E as e so E is e and I is squared minus one those are the two that we don't allow that's constants yeah hopefully that answers your question Jen the tasks from the first webinar session are available on the lacell website and I can drop you the link to those tasks into the chat but I know that there is a Dropbox link which will automatically down load those documents for years so if I can find the week one fast but there's the link to where the materials are hosted on the less out sites hopefully you are going to find the documents really useful they do have the step-by-step how-to instructions and the tasks at the end so hopefully you can work through those and don't might be able to go over some of the missing parts from this session at the start of the next session where we're going to look in a bit more detail but hopefully you've got the afternoon where you can have a bit of a play I'll just quickly summarize what we got we've done today we start off with the triangle properties and the straight lines if you remember that's 3d objects left over in the first session then we had a look at y equals MX plus C and making sure that they had really understood what the meaning of M and C is simultaneous equations quadratic functions moving them up and down and left and right and completing the square drawing cubics reciprocals and exponential functions and your homework is are these tasks that we haven't got around to today unfortunately but the graphs of inverse funk it's a very important fairly new topic to GCC but uses a really lovely feature of creating attribute points which will explain at the next session trig graphs of course very important that they understand how those work and the concept of gradient without using the calculus word is another weight lovely way to show it using a skier up and down this graph but every well that that's the end of this session early I'll leave Rob to close it down Chris hopefully we'll be able to get a link to the YouTube recording added to the site as well and that can probably happen later today I'm glad that you enjoyed using the constant controller hopefully you did find the session useful and the documents are usually available on the day of the session it gives us a chance to run through the how-to and the tasks on the day and but we hopefully will have them to you about an hour before the course starts so you've got chance to download them and read through again a very useful session hopefully thanks to Doug and hope you enjoy doing your homework tasks and hopefully next week we all be able to show you how we're using autograph within the complete math platform so fingers crossed for a bit of their autograph with incomplete maths demonstration thank you again for coming and we look forward to seeing you next time when we're going to hopefully show you some more interesting autograph their information and tasks