Question

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function . In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?

Answer 1

Your equation didn't show up. I'm assuming it is \(h(t)=-16t^2+36t\). The x-value of the maximum/minimum (depending on the a-value) of a parabola \(ax^2+bx+c\) is \(\frac{-b}{2a}\). So, in the problem you have, b=36 and a=-16. Use those values to find the time at which the ball is at its maximum. Then, plug that value in for t and solve for h(t).