The height in feet of a golf ball that is hit from the ground can be modeled by the function f(x) -16x2+96x, 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.

The maximum height of 144 feet is reached at 3 seconds.  The ball is in the air for 6 seconds.

Step-by-step explanation:

Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.  

The general form for a quadratic equation is ax² + bx + c,

here a is -16, and b is 96

To find the x coordinate of the vertex, use   x = -b/(2a)

We have x = -96/[2(-16)]

                x = -96/-32

                         x= 3

So at 3 seconds, the ball reaches it's maximum height

Now plug that into the equation to find the y value, which will be the height...

y = -16(3)² + 96(3)

     y = -16(9) + 288

     y = -144 + 288

       y =  144

To determine how long the ball is in the air, solve the equation for zero,

0 = -16x² + 96x

    0 = x² - 6x           (divide both sides by -16)

           0 = x(x - 6)

               x = 0

            x - 6 = 0,    so x = 6