Though a graphing calculator is capable of advanced mathematical computations and statistical data analysis, students commonly use these devices to draw the graphs of functions. For students interesting in becoming better acquainted with their calculator's functions- or who simply enjoy combining math and art, a graphing calculator is a great tool for making pictures.
TL;DR (Too Long; Didn't Read)
A graphing calculator can plot the curves of several equations in a single viewing window, making it possible to draw recognizable pictures. You can use the "Y" key to input the equations of several semicircles into the calculator to draw a smiley face on your calculator's graphing window.
Open the function input menu
Enter equations to make a circle
Use equations to draw the mouth
Use equations to draw a right eye
Use equations to draw a left eye
Scale your smiley face drawing
Remove the axes
If you are using an online calculator like the Desmos Graphing Calculator or some other calculator that lacks the "Y" key, you can simply type the equations in each blank field.
Press the "Y=" key to access the function input menu. This is where you will type the circle equations to make the smiley face on your graphing calculator.
Enter the equation "sqrt(100-x2)" in the field labeled "Y1" and the equation "-sqrt(100-x2)" in the field labeled "Y2." These are equations for semicircles with a radius of 10 and together they form the border of the face. The first equation generates the top half of the circle while the second generates the bottom half.
Enter "-sqrt(49-x2)" in the field marked "Y3." This semicircle forms the smiling mouth.
Enter the equations "3+sqrt(4-(x-4)2)" and "3-sqrt(4-(x-4)2)" in the fields labeled "Y4" and "Y5." This forms the right eye.
Enter the equations "3+sqrt(4-(x+4)2)" and "3-sqrt(4-(x+4)2)" in the fields labeled "Y6" and "Y7." This forms the left eye.
Press the "Zoom" key and select "Zoom Square" from the drop-down menu. This removes the scaling distortion from the viewing window.
Press the "Window" key, highlight "Format" and select the "Axes Off" option. This removes the x and y axes from the graphing window so that your smiley face is unobstructed.
While the designers of your graphing calculator surely intended more direct mathematical applications for the tool, learning how to use your calculator to draw a smiley face is actually a great way to become familiar with its functions. Plus, making math class fun is a valuable goal all on its own.