Results 1 to 3 of 3

Math Help - How to graph this polynomial function?

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    How to graph this polynomial function?

    How do i sketch the graph

    a(x-A)^2(x-b)^3(x-c)(x-d)^4 .The graph crosses y axis at E

    then there is a diagram

    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting
    Attached Thumbnails Attached Thumbnails How to graph this polynomial function?-img-20120930-00130.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,840
    Thanks
    677

    Re: How to graph this polynomial function?

    Hey skg94.

    If you have a function in this form, then it makes graphing a lot easier.

    I don't know where the turning points will be between the points A and B and also for C and D but basically the curve will be > 0 between B and C, past D, and before A, and < 0 between A and B and also between C and D, It will be zero at all the points A,B,C,D since if you plug in that value for x you will get 0 since 0 * anything = 0.

    As for where the turning points are (i.e. where the graph turns around from decreasing to increasing or increasing to decreasing), you need to use calculus for that.

    But in terms of the graph you know where its positive and negative and you also know that it has to go through the y-intercept point E as well so all this information gives a rough sketch of the graph.

    Did they cover how to get the turning points in your class or do you just need to draw a rough sketch?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,809
    Thanks
    701

    Re: How to graph this polynomial function?

    Hello, skg94

    How do I sketch the graph?

    . . y \;=\;a(x-A)^2(x-B)^3(x-C)(x-D)^4

    The graph crosses the y-axis at E.
    Code:
                          |
                        E o
                          |
                          |
          - - o - - - -o- | -o- - - - o - -
              A        B  |  C        D
                          |

    The graph has x-intercepts at x = A and x = D.
    Since their factors have even powers, the graph is tangent to the x-axis.

    The graph has x-intercepts at x = B and x = C.
    Since their factors have odd powers, the graph passes through the x-axis.


    Therefore, the graph looks like this:
    Code:
                          |
                          o
                        * | *
                          |
          - - o - - - -o- | -o- - - - o - - 
            * A *     *B  |  C*     * D *
           *     *   *    |    *   *     *
                   *      |      *
          *               |               *
                          |
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Analyze and graph the polynomial function?
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: June 27th 2012, 06:56 PM
  2. Analyze and graph another polynomial function?
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: June 27th 2012, 09:00 AM
  3. polynomial graph
    Posted in the Algebra Forum
    Replies: 9
    Last Post: March 18th 2010, 01:37 PM
  4. Graph of a polynomial function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 3rd 2009, 01:18 PM
  5. Graph Polynomial question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2009, 08:54 PM

Search Tags


/mathhelpforum @mathhelpforum