Question

find the zeros for the polynomial function and give the multiplicity for each zero. state whether the graph crosses the x-axis or touches the x-axis and turns around at each zero.

\\(f(x) = 6(x - 9)(x + 2)^3\\)

determine the zero(s).

the zero(s) is/are 9, -2.
(type integers or decimals. use a comma to separate answers as needed.)

determine the multiplicities of the zero(s). select the correct choice below and, if necessary, fill in the answer box(es) within your choice.

a. there are three zeros. the multiplicity of the largest zero is the multiplicity of the smallest zero is the multiplicity of the other zero is
(simplify your answers.)

b. there is one zero. the multiplicity of the zero is
(simplify your answer.)

c. there are two zeros. the multiplicity of the largest zero is 1. the multiplicity of the smallest zero is 3.
(simplify your answers.)

determine the behavior of the function at each zero. select the correct choice below and, if necessary, fill in the answer boxes within your choice.

a. the graph touches the x-axis and turns around at all zeros.

b. the graph crosses the x-axis at all zeros.

c. the graph crosses the x-axis at x = and touches the x-axis and turns around at x =
(simplify your answers. type integers or decimals. use a comma to separate answers as needed.)

Explanation:

Identify the zeros and their multiplicities

Using the Polynomial Functions and Multiplicity of Zeros knowledge points

$$
LATEXBLOCK0
$$

Determine the behavior at each zero

Using the Graph Behavior at Zeros knowledge point

$$
LATEXBLOCK1
$$

Select the correct multiple-choice option

Using the Graph Behavior at Zeros knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) The graph touches the x-axis and turns around at all zeros.
• (B) The graph crosses the x-axis at all zeros. (Correct answer)
• (C) The graph crosses the x-axis at x = [ ] and touches the x-axis and turns around at x = [ ]