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The graph provided shows the function \( f(x) = x^2 \), which is a basic parabola centered at the origin. You are asked to shift this graph 2 units to the right.

When shifting a function horizontally, the general transformation is:

\[
f(x - h)
\]

Where \( h \) is the horizontal shift. In this case, the shift is 2 units to the right, so the new function becomes:

\[
f(x) = (x - 2)^2
\]

Thus, after shifting the graph 2 units to the right, the transformed function is:

\[
f(x) = (x - 2)^2
\]

Would you like more details or explanations?

Here are five related questions you might find helpful:

1. How would the function change if the shift was 3 units to the left instead?
2. What happens if you apply a vertical shift instead of a horizontal one?
3. How does the vertex of the parabola change with horizontal shifts?
4. Can you describe how stretching or compressing affects the graph?
5. What if we shift the graph vertically and horizontally simultaneously?

**Tip:** Remember, shifting right is done by subtracting a positive value from \( x \), while shifting left is done by adding a value.

Move the slider so that the graph of y = x^2 gets shifted to the right 2 units. Then type the new function f(x) in the answer box.

Learn how to horizontally shift the quadratic function f(x) = x^2 by 2 units to the right. This problem involves key algebraic concepts, including function transformations and quadratic equations. Suitable for students in Grades 8-10.

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