Question

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 choose an answer.

options in drop-down menu:
(2,2)
(2,-2)
(-2,-2)
(-2,2)

Explanation:

🆕 New Concept Discovered: Graphing Absolute Value Functions
Find the turning point of a V-shaped graph.

Step 1: Identify the standard vertex form

The standard vertex form of an absolute value function is:

$$ f(x) = a|x - h| + k $$

where the point \( (h, k) \) represents the vertex (the sharp turning point of the V-shaped graph).

Step 2: Match the given function to the standard form

We are given the function:

$$ f(x) = |x + 2| - 2 $$

To match this with the standard form \( a|x - h| + k \), we rewrite the expression inside the absolute value:

$$ f(x) = 1 \cdot |x - (-2)| + (-2) $$

By comparing the terms, we find:

• \( h = -2 \)
• \( k = -2 \)

Step 3: Determine the vertex coordinates

The vertex \( (h, k) \) is:

$$ (-2, -2) $$

Answer:

(-2,-2)