The standard (vertex) form of of a quadratic equation is . Formula used .
When exploring the inverse of a quadratic equation the domain of the function must be greater or equal to zero. h>=0
Adjust the sliders a, h, and k to create the quadratic equation that you wish to explore.
The check boxes are for two points that are selected on the graph. These points will allow the exploration of points on the graph by selecting box A or B. Select the x=y check box with the move arrow to see the identity function. The point I is the inverse point of A and J for B; i.e., the x- & y-coordinates are swapped (interchanged).

If you connect points A & I or B & J, what angle is formed with the identity function in green dashes.
This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers with a worksheet to be complete for a grade.