Graphing Calculator Drawing: Roots
Roots can be used to draw deer.
This post is part of the book Graphing Calculator Drawing Exercises. Suggested citation: Skycak, J. (2019). Graphing Calculator Drawing: Roots. In Graphing Calculator Drawing Exercises. https://justinmath.com/graphing-calculator-drawing-roots/
Setup. Navigate to https://www.desmos.com/calculator. Be sure to sign in so that you can save your graph.
Demonstration - Root Graph. Observe the graph as you type each of the following inputs. In general, the graph $y=m\sqrt{x-a}$ makes an “r” shape that is shifted right $a$ units and stretched vertically by a factor of $m.$
Demonstration - Reflections. Observe the graph as you type each of the following inputs. In general, the graph $y=\sqrt{-(x-a)}$ is the graph of $y=\sqrt{x-a}$ reflected over the y-axis, and the graph of $y=-\sqrt{x-a}$ is the graph of $y=\sqrt{x-a}$ reflected over the x-axis.
Exercise. Reproduce the graph shown below using a square root function of the form $y=m\sqrt{x-a}+b.$ This will form the back of a “root deer.”
![image](https://justinmath.com/files/blog/graph-root-deer-back.png)
Exercise. Draw the back hip of the deer using a root function, and the back leg of the deer using a line.
![image](https://justinmath.com/files/blog/graph-root-deer-back-hip.png)
Exercise. Complete the back leg of the deer.
![image](https://justinmath.com/files/blog/graph-root-deer-back-hip-leg.png)
Exercise. Use another root function to draw the belly of the deer.
![image](https://justinmath.com/files/blog/graph-root-deer-back-hip-leg-belly.png)
Exercise. Use lines and a parabola to draw the front leg of the deer.
![image](https://justinmath.com/files/blog/graph-root-deer-without-head.png)
Exercise. Break the belly of the deer into two separate functions so that it does not cross over the deer’s front leg.
![image](https://justinmath.com/files/blog/graph-root-deer-without-head-2.png)
Exercise. Draw the head of the deer using two root functions.
![image](https://justinmath.com/files/blog/graph-root-deer-without-antlers.png)
Exercise. Draw antlers on the deer. You can use a root function for the upper antler, and a parabola for the lower antler.
![image](https://justinmath.com/files/blog/graph-root-deer-partial-antlers.png)
Exercise. Use a root function to draw an upper branch of antlers on each of the antlers previously drawn.
![image](https://justinmath.com/files/blog/graph-root-deer-partial-antlers-2.png)
Exercise. Use a parabola to draw a lower branch of antlers below each of the antlers previously drawn.
![image](https://justinmath.com/files/blog/graph-root-deer-full-antlers.png)
Exercise. Use lines and a parabola to complete the face of the deer.
![image](https://justinmath.com/files/blog/graph-root-deer-full-antlers-face.png)
Challenge. Draw another woodland creature, such as a hedgehog.
This post is part of the book Graphing Calculator Drawing Exercises. Suggested citation: Skycak, J. (2019). Graphing Calculator Drawing: Roots. In Graphing Calculator Drawing Exercises. https://justinmath.com/graphing-calculator-drawing-roots/