Question

for the polynomial function \\(f(x) = -x^2(x - 3)(x + 5)\\), answer parts a through e.

the y-intercept is 0.
(simplify your answer.)

d. determine whether the graph has y-axis symmetry, origin symmetry, or neither. choose the correct answer below.
a. the graph of f is symmetric about the y-axis.
b. the graph of f is symmetric about the origin.
c. the graph of f is neither symmetric about the y-axis nor symmetric about the origin.

e. if necessary, find a few additional points and graph the function. use the maximum number of turning points to check whether it is drawn correctly. choose the correct graph below.

Explanation:

Analyze symmetry of the function

Using the Symmetry of Functions and Even and Odd Functions knowledge points

$$
LATEXBLOCK0
$$

Determine polynomial end behavior

Using the End Behavior of Polynomials knowledge point

$$
LATEXBLOCK1
$$

Analyze behavior at the zeros

Using the Multiplicity of Zeros knowledge point

$$
LATEXBLOCK2
$$

Identify the correct graph

Using the End Behavior of Polynomials and Multiplicity of Zeros knowledge points

$$
LATEXBLOCK3
$$

Answer:

Question d

• A. The graph of f is symmetric about the y-axis.
• B. The graph of f is symmetric about the origin.
• C. The graph of f is neither symmetric about the y-axis nor symmetric about the origin. (Correct answer)

Question e

• A. Graph showing left end pointing up, right end pointing down.
• B. Graph showing both ends pointing up.
• C. Graph showing left end pointing down, right end pointing up.
• D. Graph showing both ends pointing down, crossing at x = -5 and x = 3, and touching at x = 0. (Correct answer)