A small ball is thrown toward an incline. This (amazing) ball bounces perfectly.
It is thrown to the right horizontally from the point (0,5) and follows the path of the parabolic equation y=5 - (x^2)/18.
The incline follows the equation y=x/2.

Find the equation of the path the ball takes after its first bounce off of the incline.

(If you wish, find some of the subsequent bounces.)
(Assume that gravity pulls straight down on the ball. Also assume the ball is not spinning so that it is perfectly reflected.)

Although I eventually figured out how to do it Charlie's way, there is an interesting connection from bounce to bounce that I exploited.

They obviously don't all reach the same height, but every one of the parabolas is tangent to the same line with slope=1/2

Specifically this tangent line is y=x/2 + 49/8

I can't prove this fact, but exploiting it does make the problem slightly easier.