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