The height of a football, in feet, t seconds after it is kicked into the air off of a tee, is modeled by the function h (t) = - 16t2 + 35t + 0.25. What is the approximate maximum height of the football?

The function is:

f (t) = - 16 t² + 35 t + 0.25

We can use the derivative:

f ' (t) = - 32 t + 35

- 32 t + 35 = 0

t = 35 : 32 = 1.09375 s

The maximum height is:

f (1.09375) = - 16 · (1.09357) ² + 35 · 1.09357 + 0.25 =

= - 19.14 + 38.28125 + 0.25 = 19.39 ft ≈ 19.4 ft.

Answer: The approximate maximum height of the ball is 19.4 ft.