Question

A ball is launched at 20 m/sec from a 50 m tall platform. The function of the ball’s height (h) at time (t) seconds after launch is h(t) = -5t^2 + 20t + 50. What is the domain of this situation?

Answer 1

you can't have a negative time, so t > 0

you also can't have a time value after the ball hits the ground (after it is launched)

so what you need to do is solve -5t^2 + 20t + 50 = 0 and determine the two roots

the larger root is going to be the largest time value possible

Answer 2

for example, if the ball hit the ground at t = 10 seconds (just randomly picking a number out of the air), then the domain would be

0 <= t <= 10

however, keep in mind that the larger root is probably not 10, so you'll have to solve for it