Question

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 36t + 10. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?

Answer 1

The ball reaches its maximum height in 1.13 seconds.

b) The ball's maximum height is 30.25 feet.

Explanation:

I had the same question and got it right

Answer 2

This sort of problem is solved easily by a graphing calculator.

a) The ball reaches its maximum height in 1.13 seconds.

b) The ball's maximum height is 30.25 feet.

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Since you want to know when and where the peak value of the function occurs, it is convenient to put it into vertex form.
h = -16(t² -(9/4)t) + 10
h = -16(t² -(9/4)t +(9/8)²) +10 +16(9/8)²
h = -16(t -9/8)² + 10 + 81/4
h = -16(t -9/8)² + 30 1/4

The vertex of the function is (9/8, 30 1/4) ≈ (1.13, 30.25).