Use an applet to explore graphical properties of fourth degree polynomials of the form
f(x) = ax^{4} + bx^{2} + c
where parameters a, b and c may be changed so that the properties of the graph of the polynomial are investigated.
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  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  Problems
Graphs of Polynomial Functions  Questions.
Factor Polynomials.
