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Math Help - Polynomial Functions

  1. #1
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    Polynomial Functions

    SOLVE.
    1 a. x^4-16=0 b. x^2=3 c. x^3=7

    Sketch the following graphs.

    2. a. f(x)=-(x-2)^2(x+3) b. (x-1)^2(x+3)(x+4)
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  2. #2
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    <br />
f(x) = -(x-2)^2 (x+3)<br />

    <br />
f(x) = -(x-2)(x-2)(x+3)<br />

    so we know our roots are at  x = -3 and a double root at  x = 2

    now using your knowledge of sketching graphs, a graph with 3 roots is going to have the shape of a sideways "S"

    create a number line with these roots and plug in values in those intervals to see the exact shape of the graph. then sketch it

    you try the next one
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  3. #3
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    Yes, I just dont know when to draw the curves on the graph since I just switched into this class. What about the first question? Do you think you can send me a website on how to draw the curves on the graph when its cubic and quartic/ and positive/negative.
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  4. #4
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    ok for the number line you have:

    < ------(-3)----------(+2)-------->

    take the equation we just created  f(x) = -(x-2)(x-2)(x+3) and plug in 3 different values from these intervals

    use the numbers (-4) , (0) , and (3) in this equation

    <---..(+)..----(-3)----..(-)..-----(+2)----..(-)..---->

    so now you know how the graph looks.
    the graph is above the x axis until it meets the root of (-3)
    then the graph is below the x axis until it meets the root of (+2) but where this is a double root, the axis then continues back down below the x axis cause a sideways "s" shape
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