f(x) = x^4 + 4x^3 - x^2 - 20x - 20

A graph of a fourth degree polynomial has a distinctive "U" shape curve like all even degreed polynomials when you look at them from a distance or use large number scales. We may focus on various regions of the graph of a polynomial and be surprised about subtle curve changes not seen in an overview. In fact, a closer view of some fourth degree polynomials may reveal a distinguishing "W" shape curve giving rise to the possibility of having four f(x) intersections with the x axis. The intersection of a polynomial function with the x axis is called a zero of the function f(x). Before progressing through these web pages try to find all the zeros of f(x). Take time to explore f(x) with paper, pencil and graphing or regular calculator now with us.
Interesting Polynomial Points In:
Region A may look like it contains only one zero of this function but it does not!
Region B has a zero of this function. Can you find it?
Region C contains a point where the curve goes across it's tangent line.
Region D has a point of f(x) that is way down low. How low?

With thanks to the following calculus one students: Gregory Atis, Lisa Khalil, Rosemary Kunz, James Munro, Deepthi R. Nallu, Paul Puricelli, Jo Schaper, Katie Sleeman, and Alex Weindel on their Summary of Curve Sketching ideas. A "Service Learning" Project to provide web pages for our community's better understanding of mathematics.