 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 Your browser is completely ignoring the tag! 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 b2 - 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 b2 - 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.