Question

The height of a ball kicked into the air from the ground can be approximated by the function
h=-5t^2 + 15t, where h is the
height in meters and t is the time in seconds.
Find the time it takes the ball to hit the ground. Show all work

Answer 1

Check the picture below, so that happens when h = 0.

$\stackrel{h}{0}~~ = ~~-5t^2+15t\implies 0=-5t(t-3)\implies 0=t(t-3)\implies t= \begin{cases} 0\\ 3~\checkmark \end{cases}$

now, notice, 0 is also a solution, which means at 0 seconds the ball was touching the ground, well, it was kicked "from" the ground, so at 0 seconds it was initially on the ground anyway.