Fourth Degree Polynomials - Applet

Use an applet to explore graphical properties of fourth degree polynomials of the form

f(x) = ax4 + bx2 + c


where parameters a, b and c may be changed so that the properties of the graph of the polynomial are investigated.

INTERACTIVE TUTORIAL

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1 - Click on the button "click here to start", above, to start the applet and maximize the window obtained.

2 - Change parameters a, b and c. Set a to 0 and b to non zero values; what is the graph of the polynomial obtained? Explain.

3 - Is the polynomial obtained even? For what values of a, b and c is the polynomial even?

4 - Change parameters a, b and c. What is the maximum number of x intercepts of the graph of the polynomial obtained? Can the polynomial have exactly two x intercepts? Can the polynomial have exactly 3 x intercepts?

5 - Set a to 1, b to 3 and c to -1. Although the quantity b
2 - 4ac is positive, the graph has only two points of intersection. Explain.

6 - Set a to 1, b to 3 and c to 1. Although the quantity b
2 - 4ac is positive, the graph no points of intersection. Explain.

7 - Set a to a positive value. What happens to f(x) as x increases? What happens to f(x) as x decreases?

8 - Set a to a negative value. What happens to f(x) as x increases? What happens to f(x) as x decreases?



More references and links to polynomial functions.

Derivatives of Polynomial Functions.

Polynomial Functions

Polynomial Functions, Zeros, Factors and Intercepts

Find Zeros of Polynomial Functions - ProblemsGraphs of Polynomial Functions - Questions.

Factor Polynomials.



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