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Math Help - Question About Parabola's

  1. #1
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    Question Question About Parabola's

    plz help me out in this

    The support for a bridge over a river is in the shape of an upside down (inverted) parabolic arch. At water level the arch is 30m wide. Max height of 10m above water. Equation?


    Equation

    y=a(x-h)2+k **the little 2 represents squared*

    what is the equation plzz need the answer quick
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  2. #2
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    Quote Originally Posted by usm_67
    plz help me out in this

    The support for a bridge over a river is in the shape of an upside down (inverted) parabolic arch. At water level the arch is 30m wide. Max height of 10m above water. Equation?


    Equation

    y=a(x-h)2+k **the little 2 represents squared*

    what is the equation plzz need the answer quick
    (h,k) is the vertex of the parabola.
    Here, the parabola is vertical and opens downward, so the vertex is the maximum height.
    (h,k) = (0,10) -------if the origin (0,0) of the x,y axes is at water level and vertically below the max height.

    y = a(x-h)^2 +k ---------(i)
    y = a(x-0)^2 +10
    y = a(x^2) +10 --------(ii)

    At righthand end of the parabola,
    x = 30/2 = 15
    y = 0
    Substitute those into (ii),
    0 = a(15^2) +10
    0 = 225a +10
    -225a = 10
    a = -10/225 = -2/45 = -1/22.5

    Therefore, if the origin (0,0) of the x,y axes is at water level and vertically below the max height, the parabola is
    y = (-2/45)x^2 +10. -------answer.
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