Question

Suppose Devin and Leslie throw a baseball into the air. The height of Devin's baseball is given by h(t)=−16t2+79t+5, where h is in feet and t is in seconds. what is the height of Devin's ball? How do you know?

Answer 1

The height of Devin's ball is h(t) = -16t^2 + 79t + 5

The maximum is reached at the vertex of the function (parabole).

The vertex is in the middle of the two roots.

To find the two roots you can use the quadratic function:

t = [-b +/-√(b^2 - 4ac)]/2a = [-79 +/- √(79^2 - 4(-16)(5))]/2(-16)

t =[-79+/-81]/-32

t = - 1/16 and t = 5

Then the vertex is at t = [5 - (-1/16) ] / 2 =  76/32

So, the maximum height is the value ox h(t) at t = 76/32.

Evaluating the function at t = 76/32, you get h(76/32) = 102.52 m.

Thas is the maximum height reached by the baseball thrown by Devin.