Question

A soccer player heads a ball from a height of 6 feet with an initial vertical velocity of 20 feet per second. The height h in feet of the ball is given by h=-16^2+20t+6 where t is the time elapsed in seconds. How long will it take the ball to hit the ground if no other players touch it?

Answer 1

WE see that at time t=0 the ball's height is 6 feet so we know the origin of our coordinates is the ground (h=0 feet)  So we need to solve this quadratic equation for the value of t that makes the equation 0.   There will be 2 solutions, one will be right and the other is usually impossible (all quadratics have two roots)
Using the quadratic formula (google it if you're unfamiliar, Brainly's math editor doesn't show things like that too nicely) I get t = 1.5s.  (the other root is -0.25)