Question

The height in feet of a soccer ball that is kicked can be modeled by the function y=-8x+24x, where x is the time in seconds after it is kicked. Find the soccer ball's maximum height and the time it takes the ball to reach this height. Then find how long the soccer ball is in the air

Answer 1

Well, your equation is linear and not quadratic. Is the -8x supposed to be squared?

Answer 2

The soccer ball's maximum height is $18feet$ and time taken to reach this height is $1.5$ seconds.

Differentiation :

The height in feet of a soccer ball is model by  a function shown below,

                        $y=-8x^{2} +24x$

where $x$ is the time in seconds after it is kicked.

To find the soccer ball's maximum height , we have to differentiate the given function with respect to x.

            $\frac{dy}{dx}=-16x+24=0\\ \\x=\frac{24}{16}=1.5seconds$

Substitute the value of $x=1.5$ in height function.

         $y(1.5)=-8*(1.5)^{2}+(24*1.5) \\\\y(1.5)=-18+36=18feet$

Thus, the soccer ball's maximum height is $18feet$ and time taken to reach this height is $1.5$ seconds.

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