To analyze the transformation from $y = x^2$ to $y = -x^2 + 9$, let's break it down step by step:

1. Reflection Over the X-Axis:
   The transformation from $y = x^2$ to $y = -x^2$ involves reflecting the parabola over the x-axis. This changes the parabola from opening upwards to opening downwards.

2. Vertical Shift:
   Adding $+9$ shifts the entire graph of $y = -x^2$ upward by 9 units.

Correct Answer:

Reflected Over the X-Axis & Shifted 9 Units Up

Would you like me to explain any part of this in more detail or explore related concepts?

Here are 5 related questions to deepen understanding:

1. What is the effect of a vertical shift on the graph of a function?
2. How do horizontal shifts differ from vertical shifts in transformations?
3. How would the transformation look if $-x^2 + 9$ was shifted 9 units to the left instead?
4. What would happen if the reflection over the x-axis was omitted from $y = -x^2 + 9$?
5. How can you identify transformations by comparing equations of two graphs?

Tip: Always follow the order of operations (reflections, shifts, stretches/compressions) when identifying transformations!