The transformation(s) applied to the graph of $y = x^2$ to obtain the black graph can be described as follows:

1. Reflection: The black graph is a reflection of the original $y = x^2$ graph across the x-axis. This changes the equation from $y = x^2$ to $y = -x^2$.

Thus, the transformation involves a reflection across the x-axis, flipping the parabola downward.

Would you like a detailed explanation of reflections or any other transformations? Let me know!

Related Questions:

1. What happens to the equation of a graph when it is reflected across the y-axis instead?
2. How can other transformations, such as translations, be combined with reflections?
3. How does a vertical stretch or compression affect a parabola’s shape?
4. Can multiple transformations be combined into a single equation? If so, how?
5. How do we graph transformations step by step to ensure accuracy?

Tip:

When identifying transformations, always consider changes to both the graph's direction and position relative to the coordinate axes.