## Graphing Polynomials By Roots

1. Start with a cubic polynomial with three roots, a,b and c.

Click on the applet to begin.

Slide the x-values of the roots of the polynomial to see how it changes the graph.

What happens when you make a double root? A triple root?

What is the end behavior of the graph? Does it change when you move the roots?

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2. Now look at a fourth degree polynomial with four roots, a,b,c and d.

Click on the applet to begin.

Slide the x-values of the roots of the polynomial to see how it changes the graph.

What happens when you make a double root? A triple root?

What is the end behavior of the graph? Does it change when you change the roots?

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3. Now look at a fifth degree polynomial with five roots, a,b,c,d and e.

Click on the applet to begin.

Slide the x-values of the roots of the polynomial to see how it changes the graph.

What happens when you make a double root? A triple root?

What is the end behavior of the graph? Does it change when the roots change?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)

John Maharry, 1/18/2007, Created with GeoGebra