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The given graph shows \( y = f(x) \), which appears to be a parabola opening upwards with its vertex at \( (0, 0) \). You are asked to determine the graph of \( y = f(x-3) - 5 \).

This transformation involves two steps:
1. **Horizontal shift**: The expression \( f(x-3) \) shifts the graph 3 units to the right.
2. **Vertical shift**: The expression \( f(x-3) - 5 \) shifts the graph 5 units downward.

### Explanation of the transformations:
- The original vertex is at \( (0, 0) \).
- After the horizontal shift of 3 units right, the new vertex becomes \( (3, 0) \).
- Then, after the vertical shift of 5 units down, the new vertex is \( (3, -5) \).

Looking at the answer choices:
- We need to find the graph where the parabola's vertex is at \( (3, -5) \), and it retains the original shape, still opening upwards.

From the given answer choices, the **third graph** from the top matches these transformations (the vertex is at \( (3, -5) \)).

### Correct answer: The third graph from the top.

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Would you like a more detailed explanation of how these transformations work? Here are some follow-up questions to enhance understanding:

1. What happens to the graph if we replace \( f(x-3) \) with \( f(x+3) \)?
2. How does multiplying the function by a negative number (e.g., \( -f(x) \)) affect the graph?
3. How would you describe a vertical stretch or compression in function transformations?
4. What is the general form of a parabolic function and how do transformations alter its vertex and axis of symmetry?
5. Can you identify how the horizontal and vertical shifts differ in their effects on the function’s equation?

**Tip**: When graphing transformations, always apply horizontal shifts before vertical ones.

Given the graph of y = f(x), determine the graph of y = f(x - 3) - 5.

Learn how to apply horizontal and vertical shifts to the graph of y = f(x) to obtain y = f(x - 3) - 5. This problem covers key concepts in function transformations, suitable for Grades 9-12.

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