word problem involving the maximum or minimum of a quadratic function

Question

A ball is thrown vertically upward. After "t" seconds, its height "h" (in feet) is given by the function h(t) = 60t-16t^2. What is the maximum height that the ball will reach?

Don't round your answer. 

Height: ____ feet 

 

Thanks!!!! :D 

Answer 1

Solve for the zeros.

 

0 = -16t² + 60t

 

0 = -4t(4t - 15)

 

t = 0        and           t = 15/4

 

Taking the average of these zeros,    t = 15/8 = 1.875

 

 

The ball reaches its maximum height in 1.875 seconds.

 

Use this fact to find the maximum height.

Answer 2

The maximum height is at the vertex of the height vs. time parabola, which is at 

 

t = -60/[2(-16)] sec = 1.875 sec

 

h_max = h(1.875) ft

 

Evaluate h(t) at t = 1.875 sec, and that will be the maximum height.  You should be able to finish from here.