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Solving Cubic equation to graph

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Graph this equation:
    P=-0.2t^3+2t^2+8t+2
    t belongs to [0,13]

    2. Relevant equations



    3. The attempt at a solution

    Can't seem to get factored to find x-int.
    and the rest of the graph.
     
  2. jcsd
  3. Sep 16, 2012 #2

    uart

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    Yep it doesn't factorize nicely. That means you can't easily find the x-intercept(s), but don't let that stop you (there may not even be any x-intercepts in your region of interest).

    Go ahead and find the start/end points plus any max/min and POIs in the given region.
     
  4. Sep 16, 2012 #3
    Im kinda math troubled like my username says lol.
    Can anyone show me the steps they took to solve this?
     
  5. Sep 16, 2012 #4

    Ray Vickson

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    Have you never, ever, drawn a graph before?

    RGV
     
  6. Sep 16, 2012 #5
    yeah my textbook doesnt describe transformations well for this chapter.
     
  7. Sep 16, 2012 #6

    Ray Vickson

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    I did not ask about "transformations". I asked you if you had ever drawn a graph. Is the answer 'yes' or 'no'?

    If you have already done similar things before, just do the same things for this problem.

    If you have not drawn a graph before (and if your book does not explain how to do it) there are numerous web pages
    that explain what to do. For example, see
    http://cstl.syr.edu/fipse/grapha/unit2/unit2.html [Broken] and
    http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i14/bk8_14i3.htm .
    In your case, however, the curve y = f(t) is not a straight line, so all you can do is make a table of some(t,y) values, and
    hand-draw a smooth curve that passes through them.

    RGV
     
    Last edited by a moderator: May 6, 2017
  8. Sep 16, 2012 #7

    Simon Bridge

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    Plot a graph of p vs t for some values of t in your range of interest.
    Stand back and look what shape it is trying to be and where it seems to be heading for the t axis. This will tell you when you are getting close to the roots.

    Particularly - plot p for t=0 and t=13 (your endpoints). If your endpoints are on opposite sides of the t axis, then there is at least one root. If p is on opposite sides of the t axis for two adjacent values of t, then there is at least one root between them.

    Use Newton-Raphson's method to get the rest of the way.

    Looks like you can find and characterize the turning points of the graph OK ... that will also give you clues.

    Or you can look up the general formula:
    http://en.wikipedia.org/wiki/Cubic_function
     
  9. Sep 16, 2012 #8

    SammyS

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    If you shift the graph down by 2 you can factor that.

    y = P(t) - 2 = -0.2t3+2t2+8t .
     
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