A large screen applet helps you explore graphical properties of third order polynomials of the form
f(x) = ax^{3} + 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
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.
