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The original function given is \( f(x) = x^2 \). The transformations applied to it are:

1. **Reflection across the x-axis**: This changes \( f(x) = x^2 \) to \( g(x) = -x^2 \).
2. **Translation 2 units to the left**: Shifting \( g(x) = -x^2 \) two units left means we replace \( x \) with \( x + 2 \), resulting in \( g(x) = -(x + 2)^2 \).

So, the transformed function would be:
\[
g(x) = -(x + 2)^2
\]

This matches answer **A**.

### Answer: A

Would you like further explanation on these transformations, or do you have any questions?

Here are some related questions you might find interesting:

1. How would the function change if it was translated to the right instead?
2. What would the equation look like if it was shifted up or down?
3. How does the reflection across the x-axis affect the graph of a parabola?
4. What if the function had been reflected across the y-axis instead?
5. How does shifting horizontally differ from shifting vertically in terms of equation changes?

**Tip:** When reflecting a function, multiplying the output by \(-1\) reflects it across the x-axis, while replacing \(x\) with \(-x\) reflects it across the y-axis.

Sharon graphed the function f(x) = x^2. She then changed the equation, and it gave her a parabola that had been reflected across the x-axis and translated 2 units to the left. What could have been her new equation?

Explore how to transform the function f(x) = x^2 by reflecting it across the x-axis and translating it 2 units to the left. Understand the resulting equation and apply key concepts in function transformations, including reflections and translations. Suitable for students in Grades 9-10.

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