Question

write your answer in the form $a|x - h| + k$, where $a$, $h$, and $k$ are integers or simplified fractions.
$g(x) = \square$

Explanation:

Step1: Identify vertex (h,k)

The vertex of the absolute value function is the corner point at $(-8, 0)$, so $h=-8$, $k=0$.

Step2: Find slope a (right side)

Use two points on the right segment: $(-8,0)$ and $(0,8)$. Calculate slope:
$$a = \frac{8-0}{0-(-8)} = \frac{8}{8} = 1$$

Step3: Substitute into vertex form

The vertex form is $a|x-h|+k$. Substitute $a=1$, $h=-8$, $k=0$:
$$g(x) = 1|x - (-8)| + 0$$

Step4: Simplify the expression

$$g(x) = |x + 8|$$

Answer:

$g(x) = |x + 8|$