Question

what is the vertex of $f(x) = |x + 8| - 3$?
$\circ$ $(-8, -3)$
$\circ$ $(-8, 3)$
$\circ$ $(8, -3)$
$\circ$ $(8, 3)$

Explanation:

Step1: Recall the vertex form of absolute value function

The general form of an absolute value function is \( f(x) = |x - h| + k \), where the vertex is \((h, k)\).

Step2: Rewrite the given function in vertex form

Given \( f(x)=|x + 8|-3 \), we can rewrite \( x + 8 \) as \( x-(-8) \). So the function becomes \( f(x)=|x - (-8)|+(-3) \).

Step3: Identify \( h \) and \( k \)

Comparing with \( f(x) = |x - h| + k \), we have \( h=-8 \) and \( k = - 3 \). So the vertex is \((h,k)=(-8,-3)\).

Answer:

\((-8, -3)\) (corresponding to the first option: \((-8, -3)\))