Question

Give an example of a quadratic function and find the inverse of that function. To earn full credit include all steps/calculations when finding the inverse. Include a graph of the function and it's inverse on the same coordinate plane.It is OK to do this work by hand and share an image of that written work.

Answer 1

Let's use the quadratic function y = x² as the example.

To find the inverse of the function, we need to switch x by y and vice-versa, then we solve for y.

So we have:

$\begin{gathered} y=x^2 \\ \\ x=y^2 \\ y=\pm\sqrt[]{x} \end{gathered}$

Now, let's graph the function y = x² (in blue) and its inverse y = ±√x (in red).

(To graph a quadratic function, we can use 5 points that are solutions to the equation. For the function y = x², we can use (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4). For its inverse, we can use (4, -2), (1, -1), (0, 0), (1, 1), (4, 2)).