Question

a ball is thrown straight up from the top of a 128 foot tall building with an initial speed of 32 feet per second. the height of the ball as a function of time can be modeled by the function h(t)=-16t+32t+128 how ling will it take for the ball to hit thr ground?

Answer 1

It will take 4 seconds for the ball to hit the ground.

Explanation:

Answer 2

Factoring, you have
h(t) = -16(t^2 -2 -8) = -16(t -4)(t +2)

The ball hits the ground when h(t) = 0, so
0 = -16(t -4)(t +2)
t = 4 or -2

The positive solution is the one of interest.
It will take 4 seconds for the ball to hit the ground.