To shift the graph of $y = x^2$ to the right by 6 units, we need to modify the function in the following way:

• The general rule for shifting a function horizontally is to adjust the $x$-value inside the function.
• To shift the graph to the right, we subtract a value from $x$. In this case, since we want to shift it 6 units to the right, we replace $x$ with $x - 6$.

Thus, the function becomes:

$y = (x - 6)^2$

This represents the graph of $y = x^2$, but shifted 6 units to the right.

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Would you like more details on horizontal shifts, or do you have other questions? Here are some related questions for further exploration:

1. How do horizontal shifts affect the graph of a function?
2. What happens if the graph is shifted to the left instead of the right?
3. How can you find the vertex of a shifted parabola?
4. How does shifting a graph affect its domain and range?
5. What other transformations can be applied to quadratic functions?

Tip: When shifting horizontally, remember that $y = (x - h)^2$ represents a shift to the right by $h$ units, and $y = (x + h)^2$ shifts it to the left by $h$ units.