Question

An outfielder throws a baseball to the player on third base. The height h of the ball in feet is modeled by the function h(t) = -16t2 + 19t + 5, where t is time in seconds. The third baseman catches the ball when it is 4 feet above the ground. To the nearest tenth of a second, how long was the ball in the air before it was caught?

Answer 1

so solve for when the ball is 4 feet from the ground

4=-16t^2 +19t +5 (-4) and (-4) on both sides
0=-16t^2 +19t +1

now use the quadratic formula \[\frac{-19 \pm \sqrt{19^2-4(-16)(1)}}{2(-16)}\]