Need help with College algebra question

Question

A ball is thrown directly upward from a height of 5ft with an initial velocity of 20ft/sec. The function ​s(t)= -16² + 20t + 5 gives the height of the​ ball, in​ feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.

The ball reaches its maximum height of ____ft, ____ ​sec(s) after the ball is thrown.

Answer 1

The equation should be s(t) -16t² + 20t +5.

The maximum height occurs when the derivative = 0, i.e. 32t=20 at t=5/8.

Substitute t=5/8 into the equation to get the maximum height.

If you have not yet had calculus, the maximum height occurs at the vertex of the parabola, i.e. at t=-b/2a=20/32.