https://file.aiquickdraw.com/mathbot/file/1729343041019x51re27d.jpg

The given function is:

\[
h(x) = (x - 5)^2 - 4
\]

This function is a transformation of the parent function \( f(x) = x^2 \), a standard quadratic function. Let's break down the transformations:

1. **Horizontal Shift**: \( (x - 5)^2 \) means that the graph of \( f(x) = x^2 \) is shifted **5 units to the right**.
2. **Vertical Shift**: The constant \( -4 \) indicates that the graph is shifted **4 units down**.
3. **No Reflection**: Since the squared term is positive, there is no reflection over the x-axis or y-axis.
4. **No Stretch or Shrink**: The coefficient of the squared term is 1, meaning there is no vertical or horizontal stretch or shrink.

Based on this analysis, the correct transformations are:

- \( D \): Shift the graph 5 units to the right.
- \( I \): Shift the graph 4 units down.

### The correct answer choices are:
- \( D \)
- \( I \)

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Would you like further explanation or details? Here are five questions you can consider next:

1. How would the graph look if we reflected it over the x-axis?
2. What would happen if the graph were stretched vertically by a factor of 2?
3. Can you describe the transformation if the function was \( h(x) = -(x + 3)^2 + 2 \)?
4. How does the horizontal shift affect the vertex of the parabola?
5. How would a horizontal shrink by a factor of 4 modify the graph?

**Tip**: When analyzing transformations of functions, always look at how the terms inside parentheses and outside constants affect the graph's shape, position, and orientation!

Use transformations of f(x) = x^2 to graph the following function h(x) = (x - 5)^2 - 4. Select all the transformations that are needed to graph the given function.

Learn how to graph the quadratic function h(x) = (x - 5)^2 - 4 using transformations of the parent function f(x) = x^2. This problem covers horizontal and vertical shifts and helps students practice graphing transformations, suitable for Grades 9-10.

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