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Math Help - The Parabola

  1. #1
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    The Parabola

    Find (a) the directrix, (b) the focus, (c) the roots of the parabola y = x^2 -5x + 4.

    I have never seen a parabola written that way.




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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    Find (a) the directrix, (b) the focus, (c) the roots of the parabola y = x^2 -5x + 4.

    I have never seen a parabola written that way.
    You're probably used to seeing the quadratic written in vertex form like:

    y=a(x-h)^2+k

    y = x^2 -5x + 4

    Now, just complete the square:

    y=\left(x^2-5x+\frac{25}{4}\right)-\frac{25}{4}+4

    y=\left(x-\frac{5}{2}\right)^2-\frac{9}{4}

    Vertex (h, k) = \left(\frac{5}{2}, -\frac{9}{4}\right)

    Directrix:

    y=k-\frac{1}{4a}

    Focus:

    \left(h, k+\frac{1}{4a}\right)

    Roots (zeros):

    x^2-5x+4=0

    Factor and solve for x.
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  3. #3
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    ok.........

    Quote Originally Posted by masters View Post
    You're probably used to seeing the quadratic written in vertex form like:

    y=a(x-h)^2+k

    y = x^2 -5x + 4

    Now, just complete the square:

    y=\left(x^2-5x+\frac{25}{4}\right)-\frac{25}{4}+4

    y=\left(x-\frac{5}{2}\right)^2-\frac{9}{4}

    Vertex (h, k) = \left(\frac{5}{2}, -\frac{9}{4}\right)

    Directrix:

    y=k-\frac{1}{4a}

    Focus:

    \left(h, k+\frac{1}{4a}\right)

    Roots (zeros):

    x^2-5x+4=0

    Factor and solve for x.
    This is exactly what confused me. I thank you for making life easy here for me.
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