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Math Help - Graphing functions that have absolute values

  1. #1
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    Graphing functions that have absolute values

    How do I graph these equations? I know what they're suppose to look like but I don't know what I'm suppose to do (with the absolute values).

    y= x^2 - 4|x| + 3

    and

    y=|x^2 - 4|x| + 3|
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mcsquared View Post
    How do I graph these equations? I know what they're suppose to look like but I don't know what I'm suppose to do (with the absolute values).

    y= x^2 - 4|x| + 3
    ok, you seem to know how to graph quadratics, so i won't address that. here is how you deal with the absolute values.

    recall the definition of absolute value:

    |x| = \left \{ \begin{array}{lr} x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.

    hence, you have to graph your function piece-wise. note that

    x^2 - 4|x| + 3 =  \left \{ \begin{array}{lr} x^2 - 4x + 3 & \mbox{ if } x \ge 0 \\ & \\ x^2 + 4x + 3  & \mbox{ if } x < 0 \end{array} \right.

    so on the interval [0, \infty) you should graph the top function, while on the interval (-\infty, 0) you should graph the bottom function

    and
    y=|x^2 - 4|x| + 3|
    take the graph you drew above, and wherever the graph is negative (below the x-axis) reflect it in the x-axis so that it is positive
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  3. #3
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    I think I get it now. Thanks a lot.
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