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 $(2, 0)$, so $h=2$, $k=0$.

Step2: Find slope a

Use point $(0,2)$ to solve for $a$:
$2 = a|0 - 2| + 0$
$2 = 2a$
$a = 1$

Step3: Substitute into form

Plug $a=1$, $h=2$, $k=0$ into $a|x-h|+k$.

Answer:

$g(x) = |x - 2|$