Question

the graph to the right is a complete graph, that is, it is continuous and displays the functions end behavior. all zeros are integers. answer the following questions.

-10, 10, 1 by -100, 100, 10

a. -2, 3, 1 (type an integers or a simplified fractions. use a comma to separate answers as needed.)
b. there are no such zeros.

(b) write an equation, expressed as the product of factors, of a polynomial that the graph might represent. use a leading coefficient of 1 or -1, and make the degree as small as possible.
\\(f(x) = (x+2)(x-1)(x-3)\\)
(type your answer in factored form.)

(c) use the equation from part (b) to find the y-intercept.
what is the y-intercept of the graph?
(type an integer or a simplified fraction.)

Explanation:

Identify the zeros and their multiplicities

Using the Multiplicity of Zeros and Graph Behavior at Zeros knowledge points

$$
LATEXBLOCK0
$$

Determine the leading coefficient sign

Using the End Behavior of Polynomials knowledge point

$$
LATEXBLOCK1
$$

Formulate the polynomial equation

Using the Polynomial Functions knowledge point

$$ f(x) = (x + 2)(x - 1)(x - 3) $$

Calculate the y-intercept

Evaluate the function at \(x = 0\):

$$
LATEXBLOCK2
$$

Answer:

(c) Use the equation from part (b) to find the y-intercept.

What is the y-intercept of the graph?

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