Question

The height of a football during a punt is modeled by h=-16t^2+60t+3. If the football hits the ground, how long did it stay in the air?

Answer 1

"how long..." is asking for time (t).  "The amount of time spent in the air" is the time from when the ball was kicked (0 seconds) to the time it landed on the ground.  Need to find the x-intercepts (one will be negative which will be invalid). You can do this by factoring ... or by using the quadratic formula. With the equation you provided, it is not factorable, so you must use the quadratic formula.

h = -16t² + 60t + 3

   a=-16   b=60  c=3

$t = \frac{-b +/- \sqrt{b^{2}-4ac } }{2a}$

$t = \frac{-60 +/- \sqrt{60^{2}-4(-16)(3) } }{2(-16)}$

$t = \frac{-60 +/- \sqrt{3600 + 192} }{-32}$

$t = \frac{-60 +/- \sqrt{3792} }{-32}$

$t = \frac{-60 +/- 61.6}{-32}$

$t = \frac{-60 + 61.6}{-32}$   or   $t = \frac{-60 - 61.6}{-32}$

$t = \frac{1.6}{-32}$        or     $t = \frac{-121.6}{-32}$

   t = -0.05            or     t = 3.8           disregard the negative

Answer: 3.8 seconds