1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Polynomial Graph Behavior

  1. Oct 26, 2008 #1


    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper behavior. No calculator allowed.


    2. Relevant equations

    3. The attempt at a solution
    Zeros: 0, 3, -2
    Degree: 1+1+1=3 (Odd)
    Leading Coefficient: 1 (Positive)
    Multiplicities: 1, 1, 1

    Therefore, I have X-Intercepts at all of the zeros. However, I am confused as to how I determine what direction the graph goes at different intervals and whether it bounces or goes through the zeros. Any help is greatly appreciated.
  2. jcsd
  3. Oct 26, 2008 #2


    User Avatar
    Homework Helper

    Find the stationary points by putting P'(x)=0
  4. Oct 27, 2008 #3
    There's a reason this is the pre-cal thread, no matter how much some like to ignore the title. Although it is a lot easier with calculus,I suggest you find out what lies in between the zeroes (positive values or negative values). In fact,as a good way to guess, pick x values halfway between the zeroes for substitution.
  5. Oct 27, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    If x> 3, then all of x, x-3, and x+2 are positive so x(x-3)(x+ 2) is positive.
    If 0< x< 3, then x and x+2 are positive but x-3 is negative so x(x-3)(x+2) is negative.
    If -2< x< 0, then x+ 2 is positive but x and x-3 are negative so x(x-3)(x+2) is positive.
    If x< -2 then all of x, x-3, and x+2 are negative so x(x-3)(x+2) is negative.

    That should be exactly what you need.
  6. Oct 27, 2008 #5


    User Avatar
    Gold Member

    What's that supposed to mean? This work is from my class, called "Honors Trigonometry and Pre-calculus."

    Thank you to HallsOfIvy and everyone else that contributed, that was exactly what I needed!
  7. Oct 27, 2008 #6
    P'(x) means the derivative with respect to x, which I am guessing you wouldn't have learned by now because that is in calculus.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Polynomial Graph Behavior
  1. On polynomials (Replies: 7)

  2. Factoring a polynomial (Replies: 4)