# Graphing Calculator Drawing: Roots

*This post is part of a series.*

** 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.”

** Exercise.** Draw the back hip of the deer using a root function, and the back leg of the deer using a line.

** Exercise.** Complete the back leg of the deer.

** Exercise.** Use another root function to draw the belly of the deer.

** Exercise.** Use lines and a parabola to draw the front leg of the deer.

** Exercise.** Break the belly of the deer into two separate functions so that it does not cross over the deer’s front leg.

** Exercise.** Draw the head of the deer using two root functions.

** Exercise.** Draw antlers on the deer. You can use a root function for the upper antler, and a parabola for the lower antler.

** Exercise.** Use a root function to draw an upper branch of antlers on each of the antlers previously drawn.

** Exercise.** Use a parabola to draw a lower branch of antlers below each of the antlers previously drawn.

** Exercise.** Use lines and a parabola to complete the face of the deer.

** Challenge.** Draw another woodland creature, such as a hedgehog.

*This post is part of a series.*