A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h (t) = - 16t^2+90t gives the height h of the ball after t seconds

a. How many seconds will it take for the ball to reach its maximum height

b. What is the maximum height of the ball

c. Give the domain and range of the function

The ball reaches a height of 126.58 ft after 2.8125 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

- (90) / 2 (-16)

-90/-32

2.8125 seconds

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

h = - 16t^2 + 90t

h = - 16 (2.8125) ^2 + 90 (2.8125)

126.58 feet