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The question asks which transformation changes the graph of \( y = x^2 \) to the graph of \( y = x^2 - 7 \).

- The transformation from \( y = x^2 \) to \( y = x^2 - 7 \) represents a **vertical translation**. Specifically, subtracting 7 from the equation means that the graph is shifted **7 units downward**.

Thus, the correct answer is:

**Translation 7 units down**.

Would you like more details or further explanation? Here are 5 related questions to expand your understanding:

1. How would the graph change if the transformation was \( y = x^2 + 7 \)?
2. What would happen to the graph of \( y = x^2 \) if we translated it 7 units to the right?
3. How can you tell the difference between horizontal and vertical translations?
4. How would the graph change if we applied a reflection instead of a translation?
5. What does it mean to apply a "dilation" to the graph of a quadratic function?

**Tip:** Remember that transformations involving "adding" or "subtracting" constants affect the graph vertically when the constant is outside the squared term (as in this case), and horizontally when the constant affects the input inside the squared term (affecting \(x\)).

Which of the following transforms the graph of y = x^2 to the graph of y = x^2 - 7?

Learn how to transform the graph of the quadratic function y = x^2 by a vertical translation of 7 units downward to get the graph of y = x^2 - 7. This concept is essential for understanding graph transformations in algebra and quadratic functions.

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