Below you'll find the solution to this question:

A toy rocket is launched from the rooftop of a building. The rocket's height, h(t), is modeled by the equation h(t) = -16t² +80t + 96 after t seconds.

1. How tall is the building?
2. How long before the rocket hits the ground at the base of the building?
3. How high will the rocket be 5 seconds after take off?
4. At what time will the rocket be 160 feet above the ground?

Answers:

1. The building is 96 feet tall.
2. 0 = (t + 1)(t - 6)  This gives us two possible answers: -1 and 6.  However, -1 seconds doesn't make sense in the context of this word problem, so the only correct answer is 6 seconds.
3. -400 + 400 + 96 = 96 feet
4. 0 = (t - 1)(t - 4)   This gives us two correct answers: 1 second and 4 seconds after takeoff.  If this doesn't make sense to you, draw a picture of the trajectory of the rocket.