The equation h=-16t^2 + 32t +9 gives the height of a ball, h, in feet above the ground, at t seconds after the ball is thrown upward. how many seconds after the ball is thrown will it reach maximum height? what is its maximum height?

H = - 16 t² + 32 t + 9
The maximum height is at the vertex of the parabola:
t = - b / (2 a ) = - 32 : ( - 32 ) = 1 s
The ball will reach maximum height in 1 second.
h max = - 16 * 1² + 32 * 1 + 9 = - 16 + 32 + 9 = 25 m
The maximum height is 25 m.