We observe that the complete height–time graph consists of four “flight” arcs, each one a downward‐opening parabola whose peak is lower than the one before.

Putting it all together, ​h(t)​ is a piecewise function made up of these four downward‐opening parabolas, each defined on one of the successive time‐intervals and each with a smaller top height than the previous one.

Thus, the motion of the ball combines what we learned about quadratic models and linear piecewise models!

We observe that the complete height–time graph consists of four “flight” arcs, each one a downward‐opening parabola whose peak is lower than the one before.

Putting it all together, ​h(t)​ is a piecewise function made up of these four downward‐opening parabolas, each defined on one of the successive time‐intervals and each with a smaller top height than the previous one.

Thus, the motion of the ball combines what we learned about quadratic models and linear piecewise models!