Sketching the Graph of Higher Degree Polynomial Functions

This video tutorial teaches how to sketch graphs of higher degree polynomials by finding zeros and determining end behavior. It covers the steps to find x-intercepts, explains the end behavior based on the degree and leading coefficient, and discusses sign changes at roots. The tutorial includes examples to illustrate these concepts, emphasizing the importance of understanding multiplicity and intervals for accurate graphing.

What are the three simple steps to find the x-intercepts of a polynomial's graph?

How do you identify the lead term of a polynomial and its effect on the graph's end behavior?

How does the end behavior of a polynomial function change based on the degree and the lead coefficient?

What is the significance of the multiplicity of a root in determining the behavior of a polynomial graph at that root?

What happens to the sign of p(x) at odd and even roots?

Explain how to determine the intervals where a polynomial function is positive or negative.

Describe the process of sketching a graph of a polynomial function based on its zeros and end behavior.