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  • 1 Post By Archie

Thread: non-x^2 subset

  1. #1
    Dec 2017
    Tel Aviv

    non-x^2 subset

    The graphs of quadratic function is subset of the set of parabolas.
    What the description (or equation) of the other subsets of the set of parabolas (that are not quadratic function)? [The complementary sets...)?
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  2. #2
    MHF Contributor
    Dec 2013

    Re: non-x^2 subset

    A general parabola can be written as $ap^2x^2+2apqxy\ +aq^2y^2+\left(bp-q\right)x+\left(bq+p\right)y+c=0$

    $p$ and $q$ determine the orientation (and scaling) of the parabola. $a$, $b$ and $c$ serve the same function (with respect to the orientation) as in $y = ax^2+bx+c$.

    See this.

    I think that restricting $p$ and $q$ to values such that $p^2+q^2=1$ removes the scaling effects of $p$ and $q$.
    Last edited by Archie; Aug 23rd 2018 at 11:47 PM.
    Thanks from topsquark
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