Given the zeros, find the end behavior to sketch the graph of a polynomial

The video tutorial covers the concepts of leading coefficients and terms in polynomials, explaining how to determine the end behavior by multiplying terms. It discusses graphing polynomials by identifying zeros and their multiplicities, and how these affect the graph's behavior. The tutorial emphasizes understanding the difference between odd and even multiplicities and how they influence whether the graph crosses or bounces at the x-axis. The session concludes with a focus on sketching polynomial graphs using these principles.

What is the leading term of the polynomial if you multiply out the expression (X + 2)^2 * X?

• X^2

• X^5

• X^3

• X^4

How does the leading term of a polynomial affect its end behavior?

• It dictates the direction the graph moves as x approaches infinity.

• It changes the graph's symmetry.

• It affects the number of zeros.

• It determines the y-intercept.

What does an even multiplicity of a zero indicate about the graph at that point?

• The graph has a vertical asymptote.

• The graph bounces off the x-axis.

• The graph has a horizontal asymptote.

• The graph crosses the x-axis.

If a polynomial has a zero at x = -1 with an odd multiplicity, what does the graph do at this point?

• The graph bounces off the x-axis.

• The graph remains constant.

• The graph crosses the x-axis.

• The graph has a cusp.

Which of the following is necessary to sketch the general shape of a polynomial graph?

• The leading coefficient only.

• Zeros, their multiplicities, and end behavior.

• The degree of the polynomial only.

• Exact y-values at all points.