Graphs of Cubic Polynomials
Author: John Maharry
Date: 1/19/2007

Click on the applet to begin.
Slide the values of the three zeros 'a','b' and 'c' to see how they change the graph.
What happens when you make a "double root"?
A triple root?

Change the Multiplicities of the factors for three values

Positive Multiplicity makes a Root

Zero Multiplicity doesn't impact the graph

Negative Multiplicity makes a Vertical Asymptote

f(x)= ( x -a )^{(Am)}  *  ( x - b )^{(Bm)} * (x - c ) ^{(Cm)}

Cm = 1 (slider from -3 to 3, step 1)
Bm = -1 (slider from -3 to 3, step 1)
a = 3 (slider from -5 to 5, step 0.1)
b = 1 (slider from -5 to 5, step 0.1)
c = -2 (slider from -5 to 5, step 0.1)
Am = 2 (slider from -3 to 3, step 1)
A: (a, 0)
B: (b, 0)
C: (c, 0)
f(x) = (x - a)^Am (x - b)^Bm (x - c)^Cm