Third Degree Polynomials - Applet

A large screen applet helps you explore graphical properties of third order polynomials of the form

f(x) = ax3 + bx + c


where a, b and c are parameters that may be changed in order to investigate their effects on the graph of the polynomial.

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 - Set c to 0 and change parameters a and b to non zero values. Is the polynomial obtained odd? For what values of a and b is the polynomial odd when c is equal to 0?

4 - Set c to a non zero value. Set a and b to non zero values is the polynomial obtained odd?

5 - Change parameters a, b and c. What is the minimum number of x intercepts of the graph of the polynomial? What is the maximum number of x intercepts? Can the polynomial have only two x intercepts?

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

7 - 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.