Question

5
select the correct answer from the drop - down menu.
consider the absolute value function $f(x)=-|x + 2|-2$.
the vertex of the function is .

Explanation:

Step1: Recall the vertex form of absolute value function

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

Step2: Rewrite the given function in the general form

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

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

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

Answer:

The vertex of the function \( f(x) = -|x + 2| - 2 \) is \((-2, -2)\).