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Thread: X-intercepts of a parabola

  1. #1
    Dec 2007

    X-intercepts of a parabola

    The vertex of a parabola is (1,2). One x-intercept is 1 + Square root 5. What is the other x-intercept? Explain.

    My first guess would be 1 - Square Root five since that's usually the outcome when you use the quadratic formula.
    However, I'm confused about where the vertex is incorporated into the answer?
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  2. #2
    MHF Contributor
    Aug 2007
    Intercepts are ALWAYS equidistant from the Axis of Symmetry.

    The vertex is (1,2) and there are two x-intercepts. This means the axis of symmetry is x = 1. Thus, 1+something and 1-something.

    As an interesting exercise, find the average (arithmetic mean) of the two roots provided by the Quadratic Formula.
    Last edited by TKHunny; Dec 26th 2007 at 04:18 AM. Reason: Change the first word from incorrect 'vertices'.
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