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22 December, 18:05

Rebekah kicks a soccer ball off the ground and in the air, with an initial velocity of 25 feet per second. Using the formula H (t) = - 16t2 + vt + s, what is the maximum height the soccer ball reaches? 9.5 feet 9.8 feet 10.2 feet 10.7 feet

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  1. 22 December, 19:48
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    H (t) = - 16t^2+25t

    The maximum height occurs at the vertex of the quadratic.

    The vertex of a quadratic is always at:

    (x, y) = (-b / (2a), (4ac-b^2) / (4a))

    So the maximum height is:

    (4ac-b^2) / (4a), and in our equation a=-16, b=25, and c=0 so

    hmax = (0-25^2) / (-64)

    hmax=-625/-64

    hmax=9.765625

    hmax≈9.8 ft (to nearest tenth of a foot)
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