Question

The height of a football, in feet, t seconds after it is kicked into the air off of a tee, is modeled by the function h(t) = –16t2 + 35t + 0.25. What is the approximate maximum height of the football?

Answer 1

The graph of the height of the football vs time is an inverted parabola, which is symmetric about its vertical axis.
When the football is first kicked, it is a height 0.25 ft, on the tee.
Just before it falls back on the ground, it is again at height 0.25 ft, as it passes by the height of the tee.
Exactly in between those two positions it is when it is at maximum height.
Set the equation equal to 0.25, the height of the tee.
Then solve for t.
You will get two values of t. t = 0, when it is first hit, and another value of t which is when the ball is again at 0.25 ft on its way down.
Then find the midpoint between t = 0 and the other values of t. (Just average the two values of t.) That is the time when the ball is at maximum height.
The last step is to evaluate the given polynomial for the time at maximum height to find the actual maximum height.