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Math Help - Number of parabollas

  1. #1
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    Number of parabollas

    How many parabollas can pass through 3 points A(x_0,y_0),B(x_1,y_1),C(x_2,y_2)
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  2. #2
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    Re: Number of parabollas

    only one
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  3. #3
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    Re: Number of parabollas

    why?
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    Re: Number of parabollas

    Quote Originally Posted by TheodorMunteanu View Post
    How many parabollas can pass through 3 points A(x_0,y_0),B(x_1,y_1),C(x_2,y_2)
    y=ax^2+bx+c

    Solve:

    \left\{\begin{matrix}y_0=ax_0^2+bx_0+c\\ y_1=ax_1^2+bx_1+c\\ y_2=ax_2^2+bx_2+c\end{matrix}\right

    And find a,b,c.
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  5. #5
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    Re: Number of parabollas

    only one parabola if the axis of symmetry is parallel to the y-axis. (not really sure about this, yet)

    if the axis of symmetry can be any line in the xy plane ... how many ???
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    Re: Number of parabollas

    Quote Originally Posted by TheodorMunteanu View Post
    How many parabollas can pass through 3 points A(x_0,y_0),B(x_1,y_1),C(x_2,y_2)
    What if A,~B,~\&,~C are collinear?
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  7. #7
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    Re: Number of parabollas

    Quote Originally Posted by Plato View Post
    What if A,~B,~\&,~C are collinear?
    A line is a degenerate form of a parabola, so it's still only one parabola.
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