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?

After 5 seconds (c)

The ball reaches a height of 29.25 ft after 1.125 seconds

Step-by-step 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