Question

Question
Which of the following is the vertex of the function f(x)=|x+12|
?(1 point)
Responses

(0,−12)
open paren 0 comma negative 1 half close paren

(0,12)
open paren 0 comma 1 half close paren

(−12,0)
open paren negative 1 half comma 0 close paren

(12,0)

Answer 1

To find the vertex of the function \( f(x) = |x + 12| \), we first recognize that the function is in the form of \( f(x) = |x - h| + k \), where \((h, k)\) is the vertex of the absolute value function.

In this case, the expression inside the absolute value \( x + 12 \) can be rewritten as \( |x - (-12)| \). This indicates that the vertex occurs at \( x = -12 \).

At \( x = -12 \), we can calculate \( f(-12) \):

\[
f(-12) = |-12 + 12| = |0| = 0
\]

Thus, the vertex of the function \( f(x) = |x + 12| \) is \((-12, 0)\).

So, the correct response is:

**(−12,0)**