Is there an equation that describes the way a ball bounces

I thought of something like this y=the absolute value of sin x^2. but that only shrinks on the x axis, I need it to shrink on the y axis (height) as well.

y1 = 3 abs cos 2x / ( 1 + x / 4)..or anything similar

Any projectile under the influence of gravity follows a parabolic shape.

So a bouncing ball would follow a series of parabolas, each with a lower maximum than the one before it.

In other words, it would be a piecewise function, rather than a single equation.

Hope this helps.