The Inverse of a Function
The blue function is quadratic, and the red function is its inverse. You can tell this because these functions are reflections of each other in the line y = x.
You can click and drag on the blue function and see how the red function (its inverse, reflected in the line y = x) follows it.
You can click and drag point P on the blue function, and it you can see the inverse of this point reflected in the line y=x.
I have put the GeoGebra tools on the applet. If you are interested in a little experimentation you can If you right click on the blue graph and select properties, then basic, and change the definition of the equation to what ever you want, and the inverse will automatically update in red.
Also note that the inverse of a quadratic function is not a function, but a relation because it fails the vertical line test, but each half of the inverse is itself a function on its own.