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Math Help - Determining Quadratic Rules

  1. #1
    Junior Member 22upon7's Avatar
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    Determining Quadratic Rules

    Hi,

    I have a test on quadratics tommorow and I need help!

    Could someone explain to me how you go about determining a quadratic rule based on coordiantes of a parabola, or point me to a helpful site/tutorial?

    Thanks,

    22upon7
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  2. #2
    Junior Member
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    this might help
    The Quadratic Formula: The Discriminant and Graphs

    http://www.purplemath.com/modules/parabola.htm

    Graphing Quadratic Functions: The Leading Coefficient / The Vertex

    Each of those has a few pages worth of information.

    If the leading coefficient is positive, it opens up.
    If the leading coefficient is negative, it opens down.
    If the discriminant is 0 you have one real root,
    If the discriminant is positive you have two real roots,
    If the discriminant is negative you have no real roots.
    Complete the square to find the vertex.
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  3. #3
    MHF Contributor
    Joined
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    Talking

    Quote Originally Posted by 22upon7 View Post
    Could someone explain to me how you go about determining a quadratic rule based on coordiantes of a parabola, or point me to a helpful site/tutorial?
    This is a fairly typical system-of-equations word problem. You plug the x- and y-coordinates of the three points into the general formula for a quadratic. This gives you three equations in terms of the (unknown) coefficients "a", "b", and "c".

    You solve the system of equations for the values of the coefficients, and thus for the required quadratic "rule".

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