how do I solve this problem im a little stuck?

Question

The height of a rocket is modeled by the equation ℎ=−16𝑡^2−48𝑡+448  where ℎ represent the height of the rocket in feet and 𝑡 represents the time after launch. Answer the following questions:

What is the height of the rocket after 3 seconds? _______ feet.

How long will it take for the rocket to land? _______seconds. 

Answer 1

Part 1: If h(t) represents the height of the rocket after t seconds, then h(3) will give the height of the rocket after 3 seconds. To compute, simply substitute t = 3:

h(3) = -16(3²) - 48(3) + 448 = 160 feet

Part 2: The rocket will land when it's height is equal to 0. In other words, we must find a value of t such that h(t) = 0.

h(t) = -16t² - 48t + 448 = 0

We can factor the polynomial such that

h(t) = -16(t² + 3 - 28) = 0

The left-hand side will equal 0 when t² + 3 - 28 = 0, so we can factor the left-hand side such that

t² + 3 - 28 = (t + 7)(t - 4) = 0

From this we can see that t = 4, because a negative time (t = -7) does not make sense in the context of the problem. Thus, the rocket will land after 4 seconds.