In this assignment, we were told to create Santa’s face using desmos.com, because it is Christmas time and we are learning about relations and functions. I included the face, nose, eyes, hat, moustache and mouth. I will be explaining some methods i used. The body was made for fun.
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So as you can see, there are a lot different functions used.
For the circles, i used x^2 +y^2<6, i use <6 because i want the circle filled in, so i tell the equation where the x and y ends. That gives us the face which is in the middle of the graph. For other circles such as eyes, and for the hat, i used the equation (x-h)^2 + (y-k)^2 <= r^2. In which i adjust the variables for the position and size of the circles. For the circle on the top of the hat, i made r :-0.5, which is the radius of the circle, and h in this case, i made it 1.5, which is the centre of the circle on the horizontal line, moves right and left as i adjust. I made the k, 4, which moves the centre of the circle up and down.
Other equations include the rim of the hat, i made 2>y>1.5 {-2.3<x<2.3}. The 2 and 1.5 is telling the vertical y where to stop, and the -2.3 and 2.3 in the brakes tells the horizontal x where to stop. I used < instead of =, which fills in the shape. The 3rd equation is y=2{-1.7<x<1.7}, which you can ignore, because it only makes a line on the rim.
One of the harder lines and equations to make was -4y=4x^2-24{-2<x<1.3}{2<y}, which makes the curved line on the right side of the hat, the longer curved line. I used the quadratic function, creating a parabola. But i needed it upside down, so i added a negative sign at the front of y, flipping it over. the 4s in front of y and x indicates where the line intercepts. So -4 in front of y creates line that reaches the -4 on the x axis. The 4 in front of x creates line that reaches 4 on the y axis. The 24 behind the x is the y intercept. The numbers in the brackets tells the x and y where to stop. That goes the same for the curved line for the moustache. Which is -7y=x^2+2{y>-1}, and for the mouth.
