Question

find g(x), where g(x) is the translation 12 units down of f(x) = -4|x + 5| + 2. write your answer in the form a|x - h| + k, where a, h, and k are integers. g(x) = \boxed{}

Explanation:

Step1: Recall vertical translation rule

For a vertical translation down by $n$ units, $g(x) = f(x) - n$.

Step2: Substitute $f(x)$ and $n=12$

$g(x) = (-4|x + 5| + 2) - 12$

Step3: Simplify the constant term

$g(x) = -4|x + 5| + (2 - 12) = -4|x - (-5)| - 10$

Answer:

$g(x) = -4|x - (-5)| - 10$