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Math Help - Introuduction to Conics problems

  1. #1
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    Introuduction to Conics problems

    I cannot understand these for the life of me.

    "Find the standard form of the equation of the parabola with its vertex at the origin"

    1. Focus (2,0)
    2. Focus: (0,-2)
    3. Directrix: Y=3
    4. Directrix: Y=-3


    "Find the Standard form of the equation of the parabola"
    1. Vertex (-1,2) Focus (-1,0)
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  2. #2
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    Quote Originally Posted by bstewart09 View Post
    I cannot understand these for the life of me.


    "Find the Standard form of the equation of the parabola"
    1. Vertex (-1,2) Focus (-1,0)
    Hi bstewart09,

    Vertex (-1, 2) means (h, k). h = -1, and k = 2 in the equation y=a(x-h)^2+k.

    Focus (-1, 0) means \left(h, k+\frac{1}{4a}\right). The parabola opens downward and k+\frac{1}{4a}=0.

    2+\frac{1}{4a}=0

    Solving the above equation for a yields a=-\frac{1}{8}

    Substituting back into the vertex form of the equation, we get:

    y=-\frac{1}{8}(x+1)^2+2

    You can convert this equation into y=ax^2+bx+c
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