Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros

The video tutorial explains how to graph higher degree polynomials by understanding their end behavior and finding their zeros. It introduces the leading coefficient test to determine end behavior and discusses methods like factoring and synthetic division to find zeros. The tutorial also covers the concept of multiplicity and its impact on graph behavior, providing a strategy for sketching polynomial graphs.

What is the primary challenge in graphing higher degree polynomials compared to lines and parabolas?

• They are always symmetrical.

• They have more x-intercepts.

• Their behavior is less predictable.

• They always have positive coefficients.

In the leading coefficient test, what does a positive leading coefficient with an odd exponent indicate about the end behavior?

• The function rises to the left and falls to the right.

• The function falls to the left and rises to the right.

• The function rises on both sides.

• The function falls on both sides.

How can the zeros of a polynomial function be graphically represented?

• As the points where the graph touches the y-axis.

• As the points where the graph crosses the x-axis.

• As the points where the graph is at its maximum.

• As the points where the graph is at its minimum.

Which method is NOT typically used to find the zeros of a polynomial function?

• Graphical estimation

• Synthetic division

• Rational roots test

• Factoring

What happens to the graph of a polynomial function at a zero with an even multiplicity?

• The graph has a vertical asymptote.

• The graph becomes a straight line.

• The graph touches the x-axis and turns around.

• The graph crosses the x-axis.

If a zero has an odd multiplicity, what is the behavior of the graph at that point?

• The graph becomes a horizontal line.

• The graph crosses the x-axis.

• The graph has a hole.

• The graph touches the x-axis and turns around.

What is the first step in the strategy for graphing higher degree polynomials?

• Determine the end behavior using the leading coefficient test.

• Find the y-intercept.

• Calculate the maximum and minimum points.

• Identify the symmetry of the graph.