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Thread: Solving Quadratic Equations by Graphing

  1. #1

    Solving Quadratic Equations by Graphing

    I am having so much difficulty understand this! I have had my teacher explain this and the tutor, and I still don't get it.

    1) x-9=0

    How do I solve this? Please tell me step by step.

  2. #2
    Senior Member
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    Re: Solving Quadratic Equations by Graphing

    1) x-9=0

    How do I solve this?
    Just replace the 0 with y, so the equation becomes

    y = x^2 - 9

    This graphs as a parabola with vertex at (0,-9) and x-intercepts at (-3,0) and (3,0). The x values at the intercepts are the solutions to the original equation. This is the graphical method of solving.

    The algebraic method is to simply factor and solve:

    x^2 - 9 = 0
    (x + 3)(x - 3) = 0
    x = 3 OR x = -3

    Hope that helps.

  3. #3
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    Re: Solving Quadratic Equations by Graphing

    [tex]x^2-9 \ = \ 0[/tex]

    [tex]x^2 \ = \ 9[/tex]

    [tex]\sqrt{x^2} \ = \ \sqrt9[/tex]

    [tex]|x| \ = \ 3[/tex]

    [tex]x \ = \ \pm3[/tex]

    [tex]See \ graph[/tex]

    [attachment=0:3ryrv9dj]zfg.jpg[/attachment:3ryrv9dj]
    Attached Images Attached Images
    I am not, therefore I do not think. Contrapositive of Descartes' quip.

  4. #4

    Re: Solving Quadratic Equations by Graphing

    Quote Originally Posted by BigGlenntheHeavy
    [tex]x^2-9 \ = \ 0[/tex]

    [tex]x^2 \ = \ 9[/tex]

    [tex]\sqrt{x^2} \ = \ \sqrt9[/tex]

    [tex]|x| \ = \ 3[/tex]

    [tex]x \ = \ \pm3[/tex]

    [tex]See \ graph[/tex]

    [attachment=0:1yuyuxjb]zfg.jpg[/attachment:1yuyuxjb]
    Thanks^^ The only thing is I just don't understand how to graph the points. And my answer comes in zeros.

  5. #5
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    Re: Solving Quadratic Equations by Graphing

    [tex]f(x) \ = \ x^2-9[/tex]

    [tex]f(3) \ = \ 0[/tex]

    [tex]f(-3) \ = \ 0[/tex]

    [tex]Hence, \ solutions \ are \ (3,0),(-3,0) \ to \ graph \ of \ f(x) \ = \ x^2-9[/tex]

    [tex]Or \ manually \ graph \ f(x) \ and \ see \ where \ the \ graph \ intercepts \ the \ x-axis.[/tex]

    [tex]At \ that \ point \ y \ = \ 0, \ so \ we \ found \ a \ solution \ of \ f(x)[/tex]
    I am not, therefore I do not think. Contrapositive of Descartes' quip.

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