Question

a baseball coach uses a pitching machine to simulate pop flies during practice. the quadratic function f(x)=-16x^2+70x+10 models the height in feet of a baseball after x seconds. how long is the baseball in the air if the ball is not caught?

Answer 1

We want to find where the function is 0.  We will use the quadratic formula to solve this:
$x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
In this equation, a=-16, b=70 and c=10:
$x= \frac{-70\pm \sqrt{70^2-4(-16)(10)}}{2(-16)} \\ \\= \frac{-70 \pm \sqrt{4900--640}}{-32} \\ \\= \frac{-70 \pm \sqrt{4900+640}}{-32} \\ \\= \frac{-70 \pm \sqrt{5540}}{-32} \\ \\= \frac{-70 \pm 74.43}{-32} = \frac{-70+74.43}{-32} \text{ or } \frac{-70-74.43}{-32} \\ \\= \frac{4.43}{-32} \text{ or } \frac{-144.43}{-32} \\ \\=-0.138 \text{ or } 4.513$
Since a negative number makes no sense in the problem situation, we have a time of 4.513 seconds.