Question

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

Explanation:

Step1: Identify vertex (h,k)

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

Step2: Find slope a

Take a point on the graph, e.g., $(2, -10)$. Substitute into $a|x-h|+k=y$:
$a|2-0| + (-8) = -10$
$2a - 8 = -10$
$2a = -2$
$a = -1$

Step3: Substitute into the form

Plug $a=-1$, $h=0$, $k=-8$ into $a|x-h|+k$.

Answer:

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