Question

what is the vertex of the function? f(x) = -2|x + 3| - 2 (3, -2) (-3, 2) (3, 2) (-3, -2)

Explanation:

Step1: Recall absolute value vertex form

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

Step2: Rewrite given function

Given \( f(x) = -2|x + 3| - 2 \), we can rewrite \( x + 3 \) as \( x - (-3) \). So the function becomes \( f(x) = -2|x - (-3)| + (-2) \).

Step3: Identify h and k

Comparing with \( f(x) = a|x - h| + k \), we have \( h = -3 \) and \( k = -2 \). So the vertex is \((-3, -2)\).

Answer:

\((-3, -2)\) (corresponding to the last option: \((-3, -2)\))