The vertical direction is modeled by:
y - k = - 193 (t - h)², for peak height k at time h.
With k = 16 inches and h = .288 sec, we have
y - 16 = - 193 (t - .288)².
Then y - 16 = - 193 (t² - .576 t + .082944).
Our vertical model is: y = - 193 t² + 111 t inches.