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

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Question 451147: A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function . What is the maximum height that the ball will reach?
h(t)=60t-16t^2
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

h(t)=60t-16t^2 |What is the maximum height that the ball will reach?

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

h(t)= -16t^2 + 60t   |completing the Square

h(t)= -16[(t-15/8)^2 - 225/64]

h(t)= -16(t-15/8)^2 + 225/4    |parabola opening downward: V(1.875,56.25)

maximum height that the ball will reach is 225/4 = 56.25 ft