Question

The height in feet of a baseball after it is hit can be modeled by the function f(x) =-16x^2 + 100x, where x is the time in seconds after the ball is hit. Find the ball's maximum height and the time it takes the ball to reach this height. Then find how long the ball is in the air.

Answer 1

h=-16x^2+100x=x(100-16x)

when is h zero? answer, when x= 100/16, and x=0

IT is a parabola, so the max apex is at 1/2 the time between the zeroes, or at time= 100/32
use that x to find max height in the original formula.

Answer 2

what you need is the vertex.

for any parabola of the form
y = ax^2 + bx + c
the x of the vertex is -b/(2a)
once you have the x of the vertex, plug into the original to get y

y will be your maximum, and it happens at the x value.
(make sure you get a max height of 156.25 ft )