https://file.aiquickdraw.com/mathbot/file/17261141617714s3ywgoc.jpg

The given graph depicts a transformation of the absolute value function, which generally follows the form:

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

We need to determine the values of \(a\), \(h\), and \(k\), based on the graph.

### Observations:
1. **Vertex (h, k)**: The vertex of the transformed absolute value function appears to be located at the point (0, 3), so \(h = 0\) and \(k = 3\).
2. **Slope (a)**: The slope of the arms of the absolute value function helps determine \(a\). From the graph, as \(x\) increases by 1, \(y\) decreases by 1 unit. This indicates that the slope of the lines is -1 (on the left) and 1 (on the right). So, \(a = -1\).

Thus, the equation for this transformed absolute value function is:

\[
y = -|x - 0| + 3 \quad \text{or} \quad y = -|x| + 3
\]

### Final Values:
- \( a = -1 \)
- \( h = 0 \)
- \( k = 3 \)

Would you like further details or clarifications on how these transformations were determined?

Here are some related questions to deepen understanding:
1. How do different values of \(a\) affect the shape of the graph?
2. What happens to the graph if \(h\) is non-zero?
3. How does \(k\) influence the vertical shift of the graph?
4. Can you describe the role of each parameter in the transformation equation?
5. How would the graph change if \(a\) were positive instead of negative?

**Tip:** When transforming absolute value functions, always look at the vertex for \(h\) and \(k\), and use the slopes to find \(a\).

Complete the equation for the transformation of the absolute value parent function y = a |x - h| + k. Determine the values of a, h, and k based on the graph provided.

Learn how to determine the equation of a transformed absolute value function from a graph. This problem involves analyzing the vertex and slope to calculate a, h, and k. Suitable for high school students (Grades 9-12).

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