Though a graphing calculator is capable of advanced mathematical computations and statistical data analysis, students mainly use these devices to draw the graphs of functions. A graphing calculator can plot the curves of several equations in a single viewing window, making it possible to draw recognisable pictures. You can input the equations of several semicircles to make a smiley face on your calculator's graphing window.

- Skill level:
- Moderate

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## Instructions

- 1
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.

- 2
Enter the equation "sqrt(100-x^2)" in the field labelled "Y1" and the equation "-sqrt(100-x^2)" in the field labelled "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.

- 3
Enter "-sqrt(49-x^2)" in the field marked "Y3." This semicircle forms the smiling mouth.

- 4
Enter the equations "3+sqrt(4-(x-4)^2)" and "3-sqrt(4-(x-4)^2)" in the fields labelled "Y4" and "Y5." This forms the right eye.

- 5
Enter the equations "3+sqrt(4-(x+4)^2)" and "3-sqrt(4-(x+4)^2)" in the fields labelled "Y6" and "Y7." This forms the left eye.

- 6
Press the "Zoom" key and select "Zoom Square" from the drop-down menu. This removes the scaling distortion from the viewing window.

- 7
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.