so when you graph, **Graph h(x)=-|x -6|+3, the 6 would be positive right?**

Yes, when graphing the function \( h(x) = -|x - 6| + 3 \), the value 6 inside the absolute value function corresponds to a **horizontal shift**. Specifically, it shifts the graph **6 units to the right**, making \( x = 6 \) the point of symmetry or the vertex.

Here’s how it breaks down:

1. **Equation breakdown:**
   - The equation \( h(x) = -|x - 6| + 3 \) is in the form \( h(x) = -|x - h| + k \).
   - \( h = 6 \), which shifts the graph 6 units to the right.
   - \( k = 3 \), which shifts the graph 3 units upwards.

2. **Vertex:**
   - The vertex of the graph will be at \( (6, 3) \).
   
3. **Reflection:**
   - The negative sign in front of the absolute value indicates a **reflection** across the x-axis. So instead of the usual V-shape opening upwards, the graph will open **downwards**.

In conclusion, the 6 inside \( |x - 6| \) does indicate a horizontal shift to the right, making it a positive shift, while the graph opens downward due to the negative sign in front of the absolute value.

Would you like to see the graph of this function?

### Related Questions:
1. How would the graph change if the equation were \( h(x) = |x - 6| + 3 \) (without the negative sign)?
2. What is the effect of changing the value of \( k \) in the equation \( h(x) = -|x - 6| + k \)?
3. How does the reflection across the x-axis affect the vertex form of the absolute value function?
4. How can you find the range of the function \( h(x) = -|x - 6| + 3 \)?
5. What happens if you change the 6 to a negative value, say \( h(x) = -|x + 6| + 3 \)?

### Tip:
The horizontal shift is always opposite in sign to the value inside the absolute value. If you see \( x - 6 \), it means a shift to the right by 6 units.

Explore the graph transformation of h(x) = -|x - 6| + 3. Understand how the value inside the absolute value function affects the horizontal shift and the graph's reflection. Learn about the vertex and how the function opens downwards. Suitable for high school students studying absolute value functions and graph transformations.

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