The function you've provided is:

\[
h(x) = -2|x - 5|
\]

This is an absolute value function that has been vertically stretched and reflected across the x-axis. Let's break it down:

1. **Absolute Value Function**: The core part is \(|x - 5|\), which means the function takes the absolute value of the expression inside the bars, ensuring that the output is always non-negative for this part.

2. **Translation**: The \((x - 5)\) indicates a horizontal shift of the function 5 units to the right. Normally, the vertex of the absolute value function \(|x|\) is at the origin, but this shifts the vertex to \(x = 5\).

3. **Vertical Stretch and Reflection**: The coefficient \(-2\) outside the absolute value means two things:
   - **Vertical Stretch**: The factor of 2 stretches the graph vertically by a factor of 2.
   - **Reflection**: The negative sign reflects the graph across the x-axis. So instead of opening upwards (like a normal absolute value function), the graph will open downwards.

### Key Points:
- The vertex of the function is at \( (5, 0) \).
- The function decreases to the left of \(x = 5\) and to the right, opening downward due to the negative coefficient.
- The slope of the lines on either side of the vertex is -2 and 2 (but since it's reflected, the lines will go down).

### Graph Behavior:
- For \(x < 5\), \(h(x) = -2(5 - x)\), which is linear with a slope of 2 but reflected downwards.
- For \(x \geq 5\), \(h(x) = -2(x - 5)\), which is linear with a slope of -2.

Would you like more details or examples on how to work with this function?

Here are some related questions you might explore:
1. How do you find the vertex of an absolute value function?
2. What is the effect of changing the coefficient of the absolute value function?
3. How does shifting a function affect its graph?
4. Can you explain how to graph an absolute value function step by step?
5. What is the domain and range of this function?

**Tip**: The absolute value function is V-shaped, and the coefficient outside determines whether it opens up or down and how steeply it grows or shrinks.

Explore how to graph and analyze the absolute value function h(x) = -2|x - 5|. Learn about vertical stretches, reflections, and horizontal translations. This problem is ideal for students in Grades 8-10.

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