Afootball is punted from a height of 8 feet above the ground with an initial vertical velocity of 44 feet per second. write an equation to model the height h, in feet, of the ball t seconds after it has been punted. the football is caught at 15 feet above the ground. how long was the football in the air?

Assuming ballistic motion, the equation for height as a function of time is
  h(t) = -16t² + v0·t + h0
where v0 is the initial vertical velocity (44 ft/s) and h0 is the initial height (8 ft).

You want to find t such that h(t) = 15. Substituting the given values, we have
  15 = -16t² +44t +8
  16t² -44t +7 = 0
Using the quadratic formula, we find t to be ...
  t = (44 ±√(44² - 4·16·7))/(2·16)
  t = (11 ± √93)/8

We are not interested in the time when the football is rising through the 15 ft height, so the time of interest is
  t = (11 +√93)/8 ≈ 2.580 . . . . seconds