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Math Help - cubic polynomials

  1. #1
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    cubic polynomials

    ok so I feel really stupid right now cause I can't figure this out:

    The graph of a cubic polynomial function has x-intercepts -3,-1,and 2. The graph also passes through the point A(1,-24)

    Determine the function in the factored form a(x-r1)(x-r2)(x-r3) where r1 ect represents the roots algebraically

    Umm How do you solve for the a value? I know its vertical strech but can't figure it out.
    Oh and I know a=3 but I can't do it algebraically
    Last edited by trouble55; May 3rd 2008 at 05:37 PM.
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  2. #2
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    Hello, trouble55!

    The graph of a cubic polynomial function has x-intercepts: -3,-1,and 2.
    The graph also passes through the point A(1,-24)

    Determine the function in the factored form: . a(x-r_1)(x-r_2)(x-r_3)
    We know the three roots, so we have: . y \;=\;a(x+3)(x+1)(x-2)\;\;{\color{blue}[1]}


    Why do you suppose they gave us another point? . A(1,\,\text{-}24)
    . . This says: when x = 1,\:y = \text{-}24

    Substitute into [1]: . \text{-}24 \:=\:a(1+3)(1+1)(1-2) \quad\Rightarrow\quad \text{-}8a \:=\:\text{-}24 \quad\Rightarrow\quad a \:=\:3


    Therefore: . y \;=\,3(x+3)(x+1)(x-2)

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  3. #3
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    Thanks,
    I can't belive it was that simple!
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