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Math Help - Dividing a parabola into 3 equivilant areas?

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    Dividing a parabola into 3 equivilant areas?

    If I have a parabola with the equation -(x-4)^2+5 how would I go about dividing it into three equal areas using two lines that meet at the same point at the top-center of the parabola and both touch the axis?

    Attached is a small illustration of what I am trying to do.
    Attached Thumbnails Attached Thumbnails Dividing a parabola into 3 equivilant areas?-parabola.gif  
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  2. #2
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    typo

    Quote Originally Posted by Shivian View Post
    If I have a parabola with the equation -(x-4)^2+5 how would I go about dividing it into three equal areas using two lines that meet at the same point at the top-center of the parabola and both touch the axis?

    Attached is a small illustration of what I am trying to do.
    1. Calculate the area included by the x-axis and the parabola. \left(\dfrac{20}3 \sqrt{5}\right)

    2. Calculate the area of the isosceles triangle.

    3. Since you already know the height of the triangle (h = 5) you can calculate the length of the base.

    4. Since the base must be symmetric to x = 4 you can get the start and endpoint of the base. I've got S(4-\frac49\sqrt{5} , 0)\  and \ E(4+\frac49\sqrt{5} , 0)
    Last edited by earboth; December 2nd 2008 at 03:58 AM.
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