Question

A ball is thrown into the air with an upward velocity of 24 ft/s. Its height h in feet after t seconds is given by the function h=-16t+24t+7. 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

The line of symmetry for the parabola described by

... y = ax²+bx+c

is given by

... x = -b/(2a)

That line for your parabola is

... t = -24/(2×(-16)) = 24/32 = 3/4 = 0.75

The vertex (maximum) lies on this line. The value of h at that point is

... h = -16(3/4)² + 24(3/4) + 7 = -9 + 18 + 7 = 16

The ball reaches its maximum height in 0.75 seconds.

The ball's maximum height is 16 ft.