https://file.aiquickdraw.com/mathbot/file/1729082016940de10w8fg.jpg

The graph shown is a V-shaped graph, characteristic of an absolute value function. The general form of an absolute value function is:

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

Where:
- \( (h, k) \) is the vertex of the graph.
- \( a \) affects the steepness and orientation of the "V".

### Step-by-step analysis:
1. **Vertex**: The vertex of the graph is located at \( (-2, -3) \) based on visual inspection.
2. **Transformation**:
   - The horizontal shift \( h \) corresponds to the x-coordinate of the vertex, so \( h = -2 \).
   - The vertical shift \( k \) corresponds to the y-coordinate of the vertex, so \( k = -3 \).
   - The graph opens upwards, so the coefficient \( a = 1 \).

### Equation form:
Since the vertex is \( (-2, -3) \), the equation of the absolute value function is:

\[
y = |x + 2| - 3
\]

Looking at the provided answer choices, the correct equation is:

\[
y - 3 = |x + 2|
\]

Thus, the correct answer is the second option from the top: **\( y - 3 = |x + 2| \)**.

Would you like more details, or do you have any further questions?

Here are some related questions for further practice:
1. What happens to the graph if we change the coefficient \( a \) to a number other than 1?
2. How does shifting the graph horizontally or vertically affect the equation?
3. How can you reflect the graph over the x-axis using the equation?
4. What is the equation of the graph if the vertex is at \( (3, 4) \)?
5. How do you determine the slope of the lines that form the "V" shape in an absolute value graph?

**Tip**: The vertex form \( y = a|x - h| + k \) is very useful for understanding shifts and transformations of absolute value graphs.

Learn how to identify the equation of an absolute value graph based on its vertex and transformations. This problem involves graphing V-shaped absolute value functions and understanding horizontal and vertical shifts. Suitable for Grades 7-9.

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