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The problem asks to choose the graph of \( g(x) = (x + 5)^2 \) and compare it to its parent function \( f(x) = x^2 \). Then, you're asked to describe the transformation.

### Step-by-step explanation:
1. **Parent Function**: The parent function \( f(x) = x^2 \) is a standard parabola with its vertex at \( (0, 0) \).

2. **Transformation in \( g(x) = (x + 5)^2 \)**:
   - The equation \( g(x) = (x + 5)^2 \) represents a **horizontal translation** of the parent function \( f(x) = x^2 \).
   - The transformation \( x + 5 \) means the graph shifts **5 units to the left**.

3. **Identifying the graph**:
   - We look for the graph that has the same shape as \( f(x) = x^2 \) but shifted 5 units left.
   - Based on the images, **Graph C** shows the correct transformation, where the parabola is shifted to the left.

4. **Correct Description**:
   - The horizontal translation of 5 units to the left is described by option **G**.

### Final Answer:
- **Graph C** and **Option G** describe the transformation of the function.

Would you like more details on transformations or any other specific questions? 

Here are some related questions to expand your understanding:
1. What is a vertical translation, and how does it affect the function?
2. How would the graph change if the equation were \( g(x) = (x - 5)^2 \)?
3. What does a horizontal stretch or compression look like for a parabola?
4. How do vertical and horizontal translations affect the vertex of a quadratic function?
5. What if the function was \( g(x) = x^2 + 5 \) instead of \( (x + 5)^2 \)?

**Tip**: Always look inside the parentheses for horizontal transformations and outside for vertical ones!

Choose the graph of g(x) = (x + 5)^2 and its parent function f(x) = x^2. Then choose the description of the transformation.

Understand the transformation of the quadratic function g(x) = (x + 5)^2 from its parent function f(x) = x^2. Learn how horizontal translations affect the graph, suitable for high school students in Grades 9-12.

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