Description: This passage is mainly about student desmos. This passage is a short tutorial on how to use desmos graphing calculator to graph conic sections, which we don’t have to install anything for it.

This is Mississauga, and I’ll be teaching you how to make simple artwork using desmos online calculators, so it’s the great thing about desmos graphing calculator, you don’t have to install anything for it, so all you need to do is to go to triple w dot desmos dot-com slash calculator, or if you can’t remember it, it’s long, go to desmos com and you’ll be taken to this page.

It says launch calculator, so press that and that launches the online graphing calculator, so it gives you this interface, so here is where you’ll be able to write down the equations for your graphs, and then it’ll automatically graph it for you, so I will recommend that you make an account, because when you make an account, that enables you to save your work, otherwise you’ll have to keep retyping and retyping your equations over and over again, and that’s tedious.

So I recommend that you make an account using whatever email you have, so first thing is this part where I teach you how to write the equations based on graphs, so you can write whatever equation you like, so let’s say I want to line, so Y is equal to 3x plus 5, so this already gives me a line, so that’s in red.

Then if you deselect the equation, it gives you that, you also have the option of choosing projector mode using this part here, but quite frankly, I’m not a big fan of projector mode unless I want my drawings to look cute or whatever, because it’s very hard to see where the intersections lie, so I’m going to turn off the ejected mode here.

So I’m going to delete this, because I am going to start making a butterfly, so I’m going to start with a semi ellipse with a vertical semi ellipse such as this, so this is x squared, so my Center is going to be at the origin, so let’s say x squared, and then I want it to go two units along the x axis, so two squared, that’s four plus y squared over, that’s five units up, so 5 squared 25 is equal to 1, so that gives us this semi ellipse.

Now it’s a little too large, so I’m going to zoom out using my click wheel, my scroll wheel, now I’m going to start making the wings using a couple of hyperbolas, so I want it to look like this, so I’m going to copy and paste this, and then I’m going to change it into 2, now I can work with this hyperbola.

But it’s a little too flat, and I want it to be fatter, so I’m going to change it, and let’s see that 16 more 8 is good, but I wand the wings to end some here, so that’s perfect, so it ends some here, so I’m going to be cutting off the hyperbola at negative four point nine five seven comma six.

So I’m going to limit our domain and range, I want everyone, I only want the X values in between negative four point nine five seven and positive four point nine five seven, so I’m going to use our curly braces, negative four point nine five seven should be less than, X should be less than positive four point nine, and there you have it, you have a hyperbola, and we’re all taking about the X values between negative four point nine five seven and positive four minus outside.

So I’m going to continue by making a semi ellipse from here, let’s see here, so that’s nine one two three four five six seven eight, that’s perfect, so my Center is going to be this, so that is negative 5 positive 2, and I’m going to be taking the left half of a semi ellipse, so that’s isolating the negative x values, so X plus 5 is equal to.

Let’s say 5 over 4 square root, so when I’m making a square root sign, I type s qrt in the square root of 16 minus y plus 1, and then squared, so you’ll notice that if you don’t put the squared sign, and that is giving you the wrong type of graph, as I have mentioned, it’s going to be negative x-values, I forget to put that in.

Now my wings are a little too fat, so I’m going to limit in this part, so it’s 5 units going to the left, and I don’t want it to be like that, I only want to come 3 units, now it’s the beautiful thing about desmos, when you’re using it on the desktop, you can copy and paste stuff, so I’m going to copy and paste this so that I can put it on this side.

Now when I put it on that side, it’s going to be the positive x values, and then I need to translate it, so I need to translate it, there are so many units to the right, and it means that it’s going to be X minus 5, that’s perfect, I’m going to use a semicircle for this part, so X plus 5 is equal to the negative square root.

My radius is going to be 2, so 2 squared 4 minus then y plus, it’s going to be here, so that’s negative function is 4 squared, then I’m going to copy and paste it, put it here, it’s going to be constant values, and then it’s going to be X minus 5, that is great, I think that looks like a great butterfly.

I’m going to end it by adding 2 and 10a here, so my antennas are going to be a couple of parabolas, so they’re going to be downward facing parabola, so it’s supposed to be X, that is squared, so X is over here, so plus 1 squared is equal to negative or no sitting around the number, that’s too low, so it has to be Y minus 6, but it’s a little too wide.

So I’m going to get rid of this, maybe negative 2, that’s perfect, that’s very convenient, and then I’m going to cut it so that we only get the Y values that are above positive 5, so with my Paris’s Y values that are above or greater than positive 5, then I’m going to copy and paste, then I’m going to change this one here and to negative 2 a minus, so now we have two unfunny, that’s great.

Now if you click Edit list, you can change the colors and the styles on your graph, so for example, I want my wings to be purple, I want my wings to be blue, and my antennas to be red, you can also change it and do it.

I want my antennas consist of broken lines, and then this is going to be blue, this is blue, everything is blue except for this, it should also be with that, and then as a body of the butterfly, I’m going to change it into edit list, I’m going to change it to orange, that’s perfect.

Now we have our finished butterfly here, we put it back to projector mode, you can see it a little bit more clearly now, and you have your list of equations here, so it’s not that hard to make a drawing based on using conic sections and decimals online calculator, so you can save it here, so it changes then for the title butterfly.