Question

what is the y-value of the y-intercept of the polynomial function $y = \frac{1}{2}(x - 8)(x + 2)$? use the keyboard to enter your answer $y = 42$

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a function is the value of \( y \) when \( x = 0 \). So we substitute \( x = 0 \) into the polynomial function \( y=\frac{1}{2}(x - 8)(x + 2) \).

Step2: Substitute \( x = 0 \)

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

$$
LATEXBLOCK0
$$

Step3: Calculate the value

First, multiply \(-8\) and \(2\): \(-8\times2=-16\). Then multiply by \(\frac{1}{2}\): \(\frac{1}{2}\times(-16)=-8\).

Answer:

\(-8\)