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Thread: General differences between quadratics and cubics

  1. #1
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    General differences between quadratics and cubics

    I am trying to summarise the differences between a general quadratic and general cubic. So far i have this:

    - A quadratic is not guaranteed to have real roots but a cubic must always have at least one
    - A quadratic will always have a turning point but a cubic is not guaranteed to
    - A quadratic will never have a point of inflexion but a cubic always will?

    Do others agree with this ( particularly the last one) and what other differences are there?
    I think there might be something about the shape but i don't know how to summarise it....

    Thoughts welcome...
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  2. #2
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    Re: General differences between quadratics and cubics

    another thought... something to do with the range of a quadratic compared to a cubic?
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  3. #3
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    Re: General differences between quadratics and cubics

    The range of a cubic is always "all real numbers". The range of a quadratic never is.
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    Re: General differences between quadratics and cubics

    There is such a thing as a standard quadratic

    $y = x^2$

    any parabola can be obtained from this standard parabola by scaling and translating (ignore rotations for the moment)

    $y=a(x-h)^2 + k$

    This isn't true for cubics. Sure there is

    $y=x^3$

    but there will be cubic curves that are not of the form

    $y = a(x-h)^3 + k$

    So a cubic curve has a richness of variety that doesn't exist for a quadratic one.
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    Re: General differences between quadratics and cubics

    Quote Originally Posted by romsek View Post
    There is such a thing as a standard quadratic

    $y = x^2$

    any parabola can be obtained from this standard parabola by scaling and translating (ignore rotations for the moment)

    $y=a(x-h)^2 + k$

    This isn't true for cubics. Sure there is

    $y=x^3$

    but there will be cubic curves that are not of the form

    $y = a(x-h)^3 + k$

    So a cubic curve has a richness of variety that doesn't exist for a quadratic one.
    An interesting observation which i have never thought about! Thanks.
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