A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 32t + 6. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
A. 1 s; 22 ft

B. 2 s; 22 ft

C. 1 s; 54 ft

D. 2 s; 6 ft

We have been given that a ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function [tex]h=-16t^2+32t+6[/tex].

a. To find the time it will take the ball to reach its maximum height, we need to find x-coordinate of vertex of our given parabola.

We will use [tex]\frac{-b}{2a}[/tex] to find the x-coordinate of vertex of our given parabola.

[tex]\frac{-32}{2\times -16}[/tex]

[tex]\frac{-2}{-2}=1[/tex]

Therefore, the ball will reach its maximum after 1 second.

b. To find the ball's maximum height we need to evaluate our given equation at [tex]t=1[/tex].

[tex]h=-16(1)^2+32(1)+6[/tex]

[tex]h=-16*1+32+6[/tex]

[tex]h=-16+32+6[/tex]

[tex]h=22[/tex]

Therefore, the maximum height of ball is 22 ft.

Upon looking at our given choices we can see that option A is the correct choice.