Quadratic Applications

Question

A ball is thrown into the air with an upward velocity of 35 ft/sec from an initial height of 4 feet. Its height h in feet after t seconds is given by the function h=-16t^2+35t+4. What is the ball’s maximum height?

Answer 1

All quadratic equations graph out as a parabola. In this case (and in all gravity related questions) the parabola is pointed down so that the vertex becomes the maximum height reached.

To find the x coordinate of the parabola use -B/2A = -35/(-16(2)) = 35/32 plug this in for x in the original equation to find the max height:

-16(35/32)² + 35(35/32) + 4 = 23.14 ft