algebra 2

The height of an arrow shot in the air is given by the function h(t)=-16t^2+144t+24, where h(t) represents the height in feet, and t represents the time in seconds.
what is the maximum height of the arrow?
how long does it take to reach the maximum height?
how long does it take the arrow to hit the ground? (round to the nearest 10th of a second)
what height was the arrow shot?

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  1. Since you labeled it algebra rather than Calculus, I will use an algebraic solution,
    completing the square

    h(t) = -16(t^2 - 9t + 81/4 - 81/4) + 24
    = -16( (t - 9/2)^2 - 81/4) + 24
    = -16(t - 9/2)^2 + 324 + 24
    = -16(t-9/2)^2 + 348

    this is a downwards-opening parabola with vertex
    (9/2 , 348)
    It will have a maximum of 348 , when t = 9/2 or 4.5 seconds

    or

    the x of the vertex is -b/(2a) = -144/-32 = 4.5
    h(4.5) = -16(20.25) + 144(4.5) + 24
    = 348

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    posted by Reiny
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