Help solving problem

Question

When a rocket is shot into the air, its height h, in feet above the ground, is a function of time t, in seconds. The height of the rocket can be found using the formula h(t) = 144t - 16t²

a. which is the rocket’s height after 5 seconds?

b. Afterhow many seconds will the rocket be at a height of 288 feet?

Answer 1

h(5) = 144(5) -16(5)^2 = 720-400 = 320 feet in 5 seconds

h(t) = 288 = 144t -16t^2

16t^2 -144t+ 288 = 0

2t^2 - 18t + 36 =0

t^2 -9t + 18 =0

(t-6)(t-3) =0

t = 3 or 6 seconds

it reaches 288 feet after 3 seconds, then keeps going up and then comes back down to 288 feet in 6 seconds