Question

Adriel kicks a football. Its height in feet is given by h, of, t, equals, minus, 16, t, squared, plus, 80, th(t)=−16t
2
+80t where tt represents the time in seconds after kick. What is the football’s greatest height?

Answer 1

h(t) = −16t^2 + 80t is a downward-opening parabola. The vertex (maximum) occurs at t = −b/(2a) = −80/(2·−16) = 2.5 s.

h(2.5) = −16(2.5)^2 + 80(2.5) = −100 + 200 = 100 feet.

So the greatest height is 100 feet (reached at 2.5 seconds).