# Graphing Calculator Drawing: Parabolas

*Parabolas can be used to draw a fish.*

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Parabolas. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-parabolas/

** Setup.** Navigate to https://www.desmos.com/calculator. Be sure to sign in so that you can save your graph.

** Demonstration - Parabola.** Observe the graph as you type each of the following inputs. In general, an absolute value graph $y=mx^2$ makes a āUā shape, with the magnitude of $m$ controlling the slope of the U, and the sign of $m$ controlling whether the U opens upward or downward.

** Demonstration - Shifts.** Observe the graph as you type each of the following inputs. In general, the graph of $y=m(x-a)^2+b$ shifts the absolute value graph $y=mx^2$ so that the hump of the āUā occurs at the point $(a,b).$

** Exercise.** Previously, you used absolute value functions to create a person. This time, draw the person using parabolas!

** Exercise.** Draw the portion of the parabola shown below.

** Exercise.** Reflect and shift a copy of the parabola portion drawn previously to form an outline of a fish.

** Exercise.** Complete the final details of the fish.

** Challenge.** Draw a school of fish! You can try to include other sea creatures, as well.

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Parabolas. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-parabolas/