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Math Help - please help sketch the graph

  1. #1
    Junior Member
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    please help sketch the graph

    Sketch the graph of y=(1+x)^2 (2-x)

    Indicate the coordinates of important points clearly.
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  2. #2
    Super Member

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    Hello, joey1!

    Sketch the graph of: . y\:=\:(1+x)^2 (2-x)
    Indicate the coordinates of important points clearly.

    By inspection, we see that the x-intercepts are: . x = \text{-}1,\;2

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

    If x = 0, then: . y = 2 . . . y-intercept (0,2)


    Using calculus, we find that x = 1 is a critical value,
    . . and that (1,4) is a maximum point.


    The graph looks like this:
    Code:
    
                          |
            *             |   (1,4)
                          |     o
             *            | *       *
              *      (0,2)o          *
                *       * |
        - - - - - - o - - + - - + - - o - -
                 (-1,0)   |         (2,0)
                          |
                          |            *
                          |
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