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Math Help - sketch cubic

  1. #1
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    sketch cubic

    Hello all, please help me

    1.) Sketch the graph of function y=4x^3 - 8x^2-11x-3
    I tried it, and got (x-3)(4x^2+4x+1) I can't factorise the quadratic to solve, need help

    2.) (3w/2 - 5/4w)^3
    Im clueless with this one i tried making the same common denominator, didnt help one bit, please provide explanation and full answers please.
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  2. #2
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    Quote Originally Posted by andrew2322 View Post
    Hello all, please help me

    1.) Sketch the graph of function y=4x^3 - 8x^2-11x-3
    I tried it, and got (x-3)(4x^2+4x+1) I can't factorise the quadratic to solve, need help
    If you can't factorise, you can always solve it using the quadratic equation. However, in this case, it can be factorised: (x-3)(4x^2+4x+1) \;\Rightarrow (x-3)(2x+1)^2

    2.) (3w/2 - 5/4w)^3
    Im clueless with this one i tried making the same common denominator, didnt help one bit, please provide explanation and full answers please
    \left(\frac{3w}{2} - \frac{5}{4w}\right)^3
    = \left(\frac{6w^2-5}{4w}\right)^3
    = \frac{1}{64w^3} (6w^2-5)^3 = 0 for x intercepts.
    But \frac{1}{64w^3} \not = 0 \Rightarrow w = 0 is an asyptote
    Therefore  (6w^2-5)^3 = 0
    6w^2-5 = 0
    w = \pm\sqrt{\frac{5}{6}}

    Now that you know the x intercepts, plot a few points, and find the limits.
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  3. #3
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    Hello, Andrew!

    1) Sketch the graph of: . y \:=\:4x^3 - 8x^2-11x-3

    I tried it and got: . (x-3)(4x^2+4x+1) . . . . Good!
    I can't factorise the quadratic. . . . . you can't?
    The function is a "positive cubic"
    . . It rises to the right and falls to the left.

    It factors to: . y \:=\:(x-3)(2x+1)^2

    The x-intercepts are: . 3\text{ and }-\frac{1}{2}

    Since the intercept x = -\frac{1}{2} has multiplicity 2,
    . . the graph is tangent to the x-axis there.


    Code:
                  |
                  |         *
                  |
               - |        *
          - - - * + - - - * - -
              *   *     * 3
             *    |  *
                  |
            *     |
                  |


    2)\;\;\left(\frac{3w}{2} - \frac{5}{4w}\right)^3

    Instructions?
    . . Are we supposed to expand and simplify it?

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  4. #4
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    Thanks

    Thanks for the help, but what's an asyptote?
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