quadratic word problem pls answer asap :D !!

Question

A toy rocket is launched vertically upward from the ground level with an initial velocity of 128 ft per seconds, then its height h, after t seconds is given by the equation h(t) = -16t² + 128t (air resistance is neglected.)

a. How long will it take the rocket to hit the maximum height?

b. What is the maximum height?

c. How long will it take to reach the ground?

d. At what time will the ball is above 192 ft?

e. Show the graph of function by the following conditions:

1. Color red for the interval time to reach above 192 ft.

2. Color blue for the interval time below 192 ft

Answer 1

h=-16t^2+128t

h'= -32t=-128

t= 128/32= 4 seconds to reach max height

max h = 128x4 - 16x4x4= 512- 256= 256 feet

2x4= 8 seconds to hit ground level

192=-16t^2+128t

16t^2-128t+192=0

t^2 - 8t + 12=0

(t-6)(t-2)=0

t=2 to 6 seconds, its above 192 feet