math

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by a quadratic function h(t) = −4.9t^2 + 9.8t + 1. What is the maximum height of the baseball?

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  1. If you know Calculus,
    h ' (t) = -9.8t + 9.8 = 0 for a max of h
    9.8t = 9.8
    t = 1

    h(1) = -4/9(1) + 9.8 + 1 = 5.9 m

    If you don't know Calculus, complete the square
    h(t) = -4.9 [t^2 - 2t +1 - 1 ] +1
    = -4.9 [ (t-1)^2 - 1 ] + 1
    = -4.9(t-1)^2 + 4.9 + 1
    = -4.9(t-1)^2 + 5.9

    so the vertex is (1,5.9) and the parabola opens downwards
    So we have a maximum of 5.9 m when t = 1 sec

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  2. Bleh

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