h(t)=-8t^2+16t+120. How to calculate this quadratic function

Question

h(t)=-8t^2+16t+120

h(t) is the height of the ball

t is the time in seconds

What is the maximum height of the ball?

What time does it reach its maximum height?

After how long will the ball hit the ground?

Answer 1

h = -8t^2 +16t + 120

h' = -16t +16 = 0

t = 1 second to reach maximum height

max height = h(1) = -8(1)^2 +16(1) + 120 = -8+16+120 = 128 feet

to reach the ground set h=0

-16t^2 + 16t + 120 = 0

divide by -16

t^2 -t -7.5 = 0

complete the square

t ^2 -t + 1/4 = 7.5 + .25

t-1/2 = sqr7.75

t = .5 + 2.784 = about 3.284 seconds to reach the ground