Question

A bottle rocket launches into the air. The equation h=-16t^2+64t+9 gives the height of the ball, h in feet, as a function of t, number of seconds after launch. What is the maximum height the ball reaches? How many seconds does it take the ball to reach that height?

Answer 1

you are basically looking for the vertex of this downwards opening parabola

the t of the vertex is -b/2a
= -64/-32 = 2 seconds

it will take 2 seconds to reach the maximum height
when t = 2
h = -16(4) + 64(2) + 9
= 73 ft

Answer 2

THANK YOU SO MUCH