Solving Quadratic Functions

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SAT Subject Test in Math II › Solving Quadratic Functions

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A baseball is thrown straight up with an initial speed of 60 feet per second by a man standing on the roof of a 100-foot high building. The height of the baseball in feet as a function of time in seconds is modeled by the function

$h(t) = -16t^{2}+60t + 100$

To the nearest tenth of a second, how long does it take for the baseball to hit the ground?

$5.0 \textrm{ sec}$

CORRECT

$1.3\textrm{ sec}$

0

$3.8\textrm{ sec}$

0

$100\textrm{ sec}$

0

$6.4\textrm{ sec}$

0

Explanation

When the baseball hits the ground, the height is 0, so we set $h\left ( t\right ) = 0$ . and solve for .

$-16t^{2}+60t + 100 = 0$

This can be done using the quadratic formula:

$t = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

Set :

$t = \frac{-60 \pm \sqrt{60^{2}-4(-16)100}}{2(-16)}$

$t = \frac{-60 \pm \sqrt{3,600- (- 6,400)}}{-32}$

$t = \frac{-60 \pm \sqrt{3,600+6,400}}{-32}$

$t = \frac{-60 \pm \sqrt{10,000}}{-32}$

$t = \frac{-60 \pm 100}{-32}$

One possible solution:

$t = \frac{-60 + 100}{-32} = \frac{40}{-32} = -1.25$

We throw this out, since time must be positive.

The other:

$t = \frac{-60 - 100}{-32} = \frac{-160}{-32} = 5$

This solution, we keep. The baseball hits the ground in 5 seconds.

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