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 + 9.

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

After 5 seconds (c)

Explanation:

Answer 2

The ball reaches a height of 29.25 ft after 1.125 seconds

Explanation:

The maximum height of a parabola can always be found by looking for the vertex. You can find the x value (or in this case the t value) of a vertex by using -b/2a in which a is the coefficient of x^2 and b is the coefficient of x.

-b/2a

-(36)/2(-16)

-36/-32

1.125 seconds

Now to find the height, we input that value in for t

h = -16t^2 + 36t + 9

h = -16(1.125)^2 + 26(1.125) + 9

29.25 feet