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:

• $D$
• $I$

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!