Question 719148
The reasonable domain would be from the time the ball is thrown, t = 0, until the time the ball comes back to the ground. When the ball comes back to the ground, its height will be 0. So to find this time we need to solve:
{{{0 = -16t^2+80t}}}
Factoring we get:
{{{0 = 16t(-t+5)}}}
From the Zero Product Property:
16t = 0 or -t+5 = 0
Solving these:
t = 0 or t = 5
We already knew about t = 0. That is when the ball is initially thrown. The t = 5 must be when it comes back to the ground. So the reasonable domain for the time would be all real numbers between 0 and 5.