Question

find the y-coordinate of the y-intercept of the polynomial function defined below. f(x) = -(5x - 5)(4x + 3)^2(5x^2 - 1)

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function \( f(x) \) occurs where \( x = 0 \). So we substitute \( x = 0 \) into the function \( f(x) \).

Step2: Substitute x = 0 into f(x)

Substitute \( x = 0 \) into \( f(x)=-(5x - 5)(4x + 3)^{2}(5x^{2}-1) \):

$$
LATEXBLOCK0
$$

Step3: Simplify the expression

First, calculate each part:

• \( 5(0)-5=-5 \), so \( -(5(0)-5)=-(-5) = 5 \)
• \( 4(0)+3 = 3 \), so \( (4(0)+3)^{2}=3^{2}=9 \)
• \( 5(0)^{2}-1=-1 \)

Now multiply them together:

$$
LATEXBLOCK1
$$

Answer:

\(-45\)