https://file.aiquickdraw.com/mathbot/file/1731553700548qd0wnyic.jpg

To determine which equation represents the graph shown, let's analyze the characteristics of the graph:

1. **Vertex Location**: The vertex (the lowest point of the V-shape) of the absolute value graph appears to be at \((-1, -4)\).
2. **Shape**: The graph has a typical V-shape, indicating it is an absolute value function of the form \( y = |x - h| + k \), where \((h, k)\) is the vertex of the graph.
3. **Equation Form**: Since the vertex is at \((-1, -4)\), we can substitute these values into the general form:
   \[
   y = |x + 1| - 4
   \]

### Matching with Options:
The correct answer is:
\[
y = |x + 1| - 4
\]

This matches the first option.

Would you like more details on how to analyze absolute value graphs, or do you have any other questions?

Here are five related questions to expand on this topic:
1. How do we identify the vertex of an absolute value function from its equation?
2. What transformations affect the shape and position of an absolute value graph?
3. How does changing the sign inside the absolute value affect the direction of the graph's "V"?
4. What are the steps to graph an absolute value function?
5. How does the slope of each side of the V in an absolute value graph relate to its equation?

**Tip:** In an absolute value function \( y = |x - h| + k \), \( h \) and \( k \) determine the horizontal and vertical shifts, moving the graph's vertex to \( (h, k) \).

The graph above is the graph of:
1. \( y = |x + 1| - 4 \)
2. \( y = |x - 1| - 4 \)
3. \( y = |x - 4| + 1 \)

Learn how to determine the equation of an absolute value graph. This problem focuses on analyzing graph shifts, identifying the vertex, and matching the graph with an equation in the form y = |x - h| + k. Suitable for students in Grades 8-10.

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