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Math Help - Completing the Square (Quadratic Polynomials)

  1. #1
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    Completing the Square (Quadratic Polynomials)

    Can someone please explain to me the steps of how to complete the square and then write the parabola y=x^2+6x+5 in the form (x-h)^2 = 4a(y-k).

    Also from this how do I find the vertex, focus and the equation of the directrix.
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  2. #2
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    Quote Originally Posted by Emililypad View Post
    Can someone please explain to me the steps of how to complete the square and then write the parabola y=x^2+6x+5 in the form (x-h)^2 = 4a(y-k).

    Also from this how do I find the vertex, focus and the equation of the directrix.
    <br />
\begin{aligned}y&=x^2+6x+5\\<br />
y-5\bold{\color{red}+9}&=x^2+6x\bold{\color{red}+9}\  \y+4&=(x+3)^2\\4 \cdot \dfrac14 (y+4)&=(x+3)^2\end{aligned}

    Therefore:

    a=\dfrac14 , h = -3, k = -4

    (h, k) is the vertex.

    a is the distance of the focus from the vertex.
    a is the distance of the directrix from the vertex in the opposite direction from the focus.
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  3. #3
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    Talking

    For further information on the general "completing the square to find the vertex" process, you can review some online resources, following through their steps on the various worked examples.
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