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Math Help - Story Problem...

  1. #1
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    Story Problem...

    An object is thrown from the origin of a coordinate system with the x-axis along the groundand the y-axis vertical. Its path, or tragectory, is given by the equation y=359x-13x^2. Find the objects maximum height.
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  2. #2
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    Hello, epetrik!

    An object is thrown from the origin of a coordinate system
    with the x-axis along the ground and the y-axis vertical.
    Its path, or trajectory, is given by the equation: . y\:=\:359x-13x^2
    Find the object's maximum height.
    Here is a non-Calculus solution . . .

    The path is a down-opening parabola; its maximum is at its vertex.

    The vertex of the parabola, y \:=\:ax^2 + bx + c, is at: . x \:=\:\frac{\text{-}b}{2a}

    We have: . a = \text{-}13,\;b = 359
    . . The vertex is at: . x \:=\:\frac{\text{-}359}{2(\text{-}13)} \:=\:\frac{359}{26}

    Then: . y \:=\: 359\left(\frac{359}{26}\right) -  13\left(\frac{359}{26}\right)^2 \:=\:\frac{128,\!881}{52}


    The maximum height is about: 2478.48 units.

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