f(t)= -5t^2 +20t
when a football is kicked with a vertical speed of 20m/s its height after t seconds is that equation but I can't understand how long the football in the air, and after how long after it has been kicked is the football at a height of 15m?

how long is the football in the air?

well, the football is in the air as long as it's not on the ground. Since f(t) is the height measurement, solve the quadratic for

0 = -5t^2 + 20t

solve for t. you will get 2 answers... one when you first kick it off the ground, the other when it lands back down to the ground.

for the second part, since f(t) is the height, substitute 15 for f(t)

15 = -5t^2 + 20t

solve for t. you will get two answers again. One answer when the ball hits 15 m while going up, and another one when the ball hits 15 m coming back down.