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