Aball 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?

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.