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We are given two functions:

- \( f(x) = x^2 \)
- \( g(x) = (x - 2)^2 - 3 \)

### Describing the transformation:

1. **Horizontal Translation**: 
   The function \( g(x) = (x - 2)^2 - 3 \) contains \( (x - 2) \) inside the square. This indicates a **horizontal translation**. Specifically, the graph is shifted **2 units to the right** compared to the graph of \( f(x) = x^2 \).

2. **Vertical Translation**: 
   The term \( -3 \) outside the square means the graph is shifted **3 units downward**.

### Filling in the blanks:
The graph of \( g \) is a translation:

- **2 units right** and
- **3 units down**

of the graph of \( f \).

Would you like a further explanation or a graph of these transformations? Here are some related questions you could explore:

1. What other transformations exist beyond translations?
2. How does the transformation affect the vertex of a parabola?
3. How would the graph look if the transformation was \( g(x) = (x + 2)^2 + 3 \)?
4. What is the general form for describing transformations of quadratic functions?
5. Can you describe a reflection transformation for a quadratic function?

**Tip**: When analyzing transformations, always look for changes to the input (horizontal shifts) and the output (vertical shifts).

Describe the transformation of f(x) = x^2 represented by g(x) = (x - 2)^2 - 3. Then identify the graph of each function.

Learn how to describe the transformation of the quadratic function f(x) = x^2 to g(x) = (x - 2)^2 - 3. This problem demonstrates key concepts of horizontal and vertical translations. Suitable for Grades 9-10 students.

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