https://file.aiquickdraw.com/mathbot/file/1729525499464wrtzqaz8.jpg

The graph shown in your image depicts a V-shaped figure, which is characteristic of an absolute value function. It appears to be shifted horizontally and vertically from the origin. 

To analyze it, the basic form of an absolute value function is:

\[
y = a |x - h| + k
\]

Where:
- \( h \) represents the horizontal shift (left or right),
- \( k \) represents the vertical shift (up or down).

### From the graph:
- The vertex of the "V" is at the point \((-2, -2)\), meaning the function has been shifted left by 2 units and down by 2 units.
- This gives us a horizontal shift of \( h = -2 \) and a vertical shift of \( k = -2 \).

Thus, the equation of the graph is:
\[
y + 2 = |x + 2|
\]

This corresponds to the correct answer from the options provided: **\( y + 2 = |x + 2| \)**.

Would you like more details or have any questions?

Here are 5 questions to expand on this topic:
1. What does the absolute value function graph look like when there are no shifts?
2. How do changes in the coefficient of the absolute value affect the graph’s steepness?
3. What is the general form of a shifted absolute value function?
4. How would the graph change if \( h = 2 \) instead of \( h = -2 \)?
5. Can you describe the transformation when the equation is \( y - 2 = |x + 2| \)?

**Tip**: To quickly determine the vertex of an absolute value graph, look at the values of \( h \) and \( k \) in the equation \( y = |x - h| + k \). The vertex will be at the point \( (h, k) \).

Learn how to identify the equation for an absolute value function graph. This problem covers key algebraic concepts, including shifts in absolute value functions and their impact on the graph. Suitable for students in Grades 9-10.

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