Question

find the y-coordinate of the y-intercept of the polynomial function defined below.\\( f(x) = -(3x - 1)(3x - 5)(x - 1) \\)

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a function \( y = f(x) \) occurs where \( x = 0 \). So we need to find \( f(0) \).

Step2: Substitute \( x = 0 \) into the function

Substitute \( x = 0 \) into \( f(x)=-(3x - 1)(3x - 5)(x - 1) \):

$$
LATEXBLOCK0
$$

Step3: Simplify the expression

First, calculate the product inside the parentheses:
\( (-1)\times(-5)=5 \), then \( 5\times(-1)=-5 \), and then we have \( -(-5) = 5 \).

Answer:

5