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Math Help - How to find a Quadratic Function when given the zeros

  1. #1
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    How to find a Quadratic Function when given the zeros

    Give a quadratic function with zeros at x=3 and x= -4.
    I know how to solve a quadratic equation, but have no idea where to begin when given the answer first.
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  2. #2
    Super Member TheChaz's Avatar
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    Re: How to find a Quadratic Function when given the zeros

    Quote Originally Posted by Ray1357 View Post
    Give a quadratic function with zeros at x=3 and x= -4.
    I know how to solve a quadratic equation, but have no idea where to begin when given the answer first.
    If x = a is a root of the polynomial, then (x - a) is a factor.
    So we have factors (x - 3) and (x - -4) = (x + 4)

    f(x) = c(x - 3)(x + 4), where c is not 0


    If you were going to solve a quadratic equation by factoring (such as x^2 - x - 6 = 0), you would use the "zero product property" to set each factor equal to zero.

    (x - 3)(x + 2) = 0 -->
    x - 3 = 0 or x + 2 = 0
    <-->
    x = 3 or x = -2.

    When you are given the roots, you reverse the process. Notice that the solutions to
    (x - 3)(x + 2) = 0 don't change if you multiply this equation by a nonzero constant, so this would give us
    c(x - 3)(x + 2) = 0 as in the given problem.
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    Re: How to find a Quadratic Function when given the zeros

    That makes complete sense, thank you!
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    Super Member TheChaz's Avatar
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    Re: How to find a Quadratic Function when given the zeros

    Quote Originally Posted by Ray1357 View Post
    That makes complete sense, thank you!
    No problemo!
    Welcome to the forums.
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