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Math Help - Quick Parabolas

  1. #1
    MHF Contributor Quick's Avatar
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    Quick Parabolas

    Sorry, your Web browser is not Java compatible. This prototype will not be of much interest to you.
    Three points define a "Quick" Parabola.

    You can move the points around and press "Activate" to see the parabola

    Two questions:

    How is it made?

    and (this one I want to know)

    Can all parabolas be quick parabolas?




    If you don't see the diagram then you can't do this.



    Press the red "X" at the bottom right corner of the diagram to remove the parabola...
    Last edited by Quick; January 20th 2007 at 02:29 PM. Reason: slowing it down
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  2. #2
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    Three points define a "Quick" Parabola
    Three non-colinear points. Because otherwise the determinant of the 3x3 linear system is zero.

    And further, some parabolas have the form,
    Ax^2+By^2+Cxy+Dx+Fy+D=0
    In that case 3 points is not sufficient.
    You need 6 (and I forgot the conditions on them).

    But for a "standard" parabola,
    y=ax^2+bx+c,a\not = 0
    You have a unique parabola.
    Last edited by ThePerfectHacker; January 20th 2007 at 02:22 PM.
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Three non-colinear points. Because otherwise the determinant of the 3x3 linear system is zero.
    Yes, I meant to say non-colinear...
    But I did not use a matrix to make them.
    And further, some parabolas have the form,
    Ax^2+By^2+Cxy+Dx+Fy+D=0
    In that case 3 points is not sufficient.
    You need 6 (and I forgot the conditions on them).
    Really? Cause it seems like it covers all the kinds of parabolas...
    Last edited by Quick; January 20th 2007 at 02:44 PM.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick View Post
    Yes, I meant to say non-colinear...
    But I did not use a matrix to make them.

    Really? Cause it seems like it covers all the kinds of parabolas...
    Select three non-colinear points. You can create one parabola through them that has a vertical axis of symmetry. You can create one parabola through them the has a horizontal axis of symmetry. You can create one parabola through them that has an axis of symmetry parallel to the line y = x. etc.

    -Dan
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