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The function given in part (b) is \( g(x) = -\frac{1}{9}x^2 \), and the problem asks about the transformation from the graph of \( y = x^2 \).

This function is a **transformation** of \( y = x^2 \), which is the standard parabola. The transformations present are:

1. **Reflection**: The negative sign in front of the function, \( -\frac{1}{9}x^2 \), reflects the parabola over the x-axis. This means the graph opens downward instead of upward.
   
2. **Vertical Compression**: The factor \( \frac{1}{9} \) causes a vertical compression. This means the parabola becomes wider, as the y-values are scaled by a factor of \( \frac{1}{9} \), making the graph less steep.

### Summary of transformations:
- **Reflection** over the x-axis.
- **Vertical compression** by a factor of 9.

This explains how \( g(x) = -\frac{1}{9}x^2 \) is related to \( y = x^2 \).

Would you like further details or clarification? Here are 5 related questions:

1. How would the graph change if the factor were \( \frac{1}{4} \) instead of \( \frac{1}{9} \)?
2. What is the effect of a horizontal stretch or compression on a graph?
3. How would the graph be transformed if the function were \( g(x) = -x^2 + 2 \)?
4. How does the value of \( a \) in \( y = ax^2 \) affect the graph’s width?
5. How would adding a constant to \( g(x) = -\frac{1}{9}x^2 \) affect its graph?

**Tip**: Always analyze the coefficients and signs in a quadratic function to understand how it will transform the basic parabola.

Explore how the quadratic function g(x) = -1/9x^2 is derived from the standard parabola y = x^2. This analysis covers the reflection and vertical compression transformations, making it ideal for high school students learning about graph transformations in Algebra.

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