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Math Help - intersection points of 2 curves

  1. #1
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    intersection points of 2 curves

    Hi everybody, this may be really simple and im just missing the point. But how can you calculate the 2 intersection points of 2 quadratics if one is x^2 and the other is -x^2?

    Many thanks

    Daniel
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  2. #2
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    Quote Originally Posted by wilsnunn View Post
    Hi everybody, this may be really simple and im just missing the point. But how can you calculate the 2 intersection points of 2 quadratics if one is x^2 and the other is -x^2?

    Many thanks

    Daniel
    Hi Daniel,

    The graph of f(x)=x^2 is a parabola with vertex at the origin and opening upward.

    The graph of f(x)=-x^2 is a parabola with vertex at the origin and opening downward.

    Their obvious intersection is the origin.
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  3. #3
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    Quote Originally Posted by wilsnunn View Post
    Hi everybody, this may be really simple and im just missing the point. But how can you calculate the 2 intersection points of 2 quadratics if one is x^2 and the other is -x^2?

    Many thanks

    Daniel
    There is only one intersection point - at the origin.

    You can find this by setting them equal to each other

    -x^2 = x^2

    2x^2 = 0

    x = 0
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  4. #4
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    Quote Originally Posted by masters View Post
    Hi Daniel,

    The graph of f(x)=x^2 is a parabola with vertex at the origin and opening upward.

    The graph of f(x)=-x^2 is a parabola with vertex at the origin and opening downward.

    Their obvious intersection is the origin.
    I meant if one was say f(x)=x^2-6x+9 and the other was f(x)=-x^2+7x-11

    How would you do it then? Sorry I should have mentioned that in the opening thread.

    Daniel
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  5. #5
    Junior Member piglet's Avatar
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    Quote Originally Posted by wilsnunn View Post
    I meant if one was say f(x)=x^2-6x+9 and the other was f(x)=-x^2+7x-11

    How would you do it then? Sorry I should have mentioned that in the opening thread.

    Daniel
     f(x) is just another name for y

    let  y = y

    =>  x^{2} - 6x + 9 = -x^{2} +7x - 11
    =>  2x^{2} - 13x + 20 = 0

    solve that quadratic for x and find the corresponding y value by subbing x into original equation of curve
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