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Math Help - Determine Equation For Polynomial Function shown by Graph

  1. #1
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    Question Determine Equation For Polynomial Function shown by Graph

    Determine an equation in factored form for the polynomial represented by the graph.

    Graph #1: Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting


    Looking at this I can say:
    >4 degree polynomial; Quartic
    >Zero's: -1, +1, 2
    >Even Degree Polynomial
    >Point at: (0,4)

    y= a (x+1) (x-1) (x-2)
    ...plug in (0,4) -> 4=a(0+1)(0-1)(0-2) -> 2=a
    y=2(x+1)(x-1)(x-2)................Is this answer correct? Shouldn't this have been an Even Degree Polynomial?(Also just making sure, is this in factored form?)

    Graph #2. Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting

    Looking at this I can say:
    >4 Degree Polynomial (minimum); Quartic
    >Zero's: -2, +1
    >Point at: (0,-2)

    y=a (x+2) (x-1)
    ...plug in (0,-2) -> -2=a (0+2)(0-1) -> 0=a -> ?
    y=(x+2)(x-1)......................I'm certain this is unfinished/incorrect
    .........................................Since a=0, and no other point in defined on the graph...? I don't know how I would solve this?
    Last edited by tdotodot; September 16th 2013 at 07:13 AM.
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  2. #2
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    Re: Determine Equation For Polynomial Function shown by Graph

    Anyone? Can you please just check the second one for me?
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  3. #3
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    Re: Determine Equation For Polynomial Function shown by Graph

    First problem: there must be four roots. since you have only three roots, the fourth cannot be complex because complex roots are in pairs of congugates. The fourth root must be pont 2 as a double root. To get the correct answer you have to square the binomial for the double root, i.e. (x-2)^2

    do the same in problem 2
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