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Math Help - Sign Graphs

  1. #1
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    Sign Graphs

    Can someone explain how to do sign graphs for inequalities?

    Like (x-3)(x+4)>0
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  2. #2
    Super Member

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    Hello, mm99!

    Can someone explain how to do sign graphs for inequalities?

    Like: .  (x-3)(x+4)\:>\:0
    Here's one way . . .

    We have the graph of: . y \:=\:(x-3)(x+4)\quad\Rightarrow\quad y \:=\:x^2+x-12

    This is an up-opening parabola.
    We want to know when this graph is positive (above the x-axis).

    Draw a sketch (or visualize it) . . .
    The x-intercepts are x = -4,\:3
    The graph is positive to the left and right of the intercepts.
    Code:
                          |
         *                |            *
                          |
          *               |           *
           *              |          *
        - - * - - - - - - + - - - - * - -
           -4 *           |       * 3
                  *       |   *
                        * |
                          |

    Therefore: . (-\infty,\:-4) \cup (3,\:\infty)

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