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Math Help - Polynomial Functions

  1. #1
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    Polynomial Functions

    Hello. I was hoping someone could help me with this problem as it relates to polynomial functions.

    A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t2 + 576t. After how many seconds does the projectile take to reach its maximum height?

    It would be nice if you could give me a full explanation as I truly want to learn how to do this. Thank you so much guys.
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  2. #2
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    Re: Polynomial Functions

    Hello, DreadfulGlory!

    A projectile is thrown upward so that its height above the ground after t seconds is given by the function:
    . . h(t) \:=\: - 16t^2 + 576t
    After how many seconds does the projectile take to reach its maximum height?

    I'll assume that you are not familiar with Calculus.

    The graph of h(t) is a down-opening parabola.
    Its maximum is at its vertex.
    The formula for the vertex is: . t \:=\:\frac{\text{-}b}{2a}

    We have: . a = -16,\;b = 576

    Hence: . t \:=\:\frac{\text{-}576}{2(\text{-}16)} \:=\:18

    The projectile takes 18 second to reach maximum height.


    [The maximum height is: . h(18) \:=\:-16(18^2) + 576(18) \:=\: 5184 units.]
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  3. #3
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    Re: Polynomial Functions

    You have another way on completing this sum using quadratic function
    h_(t)=-16t^2+576t
    h_((t) )=-16(t^2-36t)
    h_((t) )=-16(t^2-36t+324-324)
    h_((t) )=-16((t-18)^2-324)
    h_((t) )=-16(t-18)^2+5184
    (h_((t) ) )_max=(-16(t-18)^2 )_min+5184

    (-16(t-18)^2 )_min=0 when t=18
    Therefore (h_((t) ) )_max=5184 units
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