I need a quadratic equation, the maximum height, and the amount of time it was in the air.

Question

a rocket was launched vertically from the ground with an initial velocity of 64 ft/sec. a) write a quadratic function h(t) that shows the height, in feet, of the rocket t seconds after it was launched. b) what is the rocket’s maximum height? c) determine the amount of time the rocket was in the air.

Answer 1

h(t) = 64t - 16t²

The maximum height will occur when the derivative of h with respect to t is 0.

If you don't know calculus, the vertex of the parabola with occur at -b/2a where a=-16 and b = 64.

The maximum height will be determined by plugging in the time when the maximum occurs into h(t).