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The image presents the parent graph \( y = x^2 \) and asks about horizontal shifts of this graph. Here's how each of the transformations affects the graph:

1. **\( y = (x + 1)^2 \)** shifts the parent graph to the **left** by **1** unit.
2. **\( y = (x + 3)^2 \)** shifts the parent graph to the **left** by **3** units.
3. **\( y = (x - 1)^2 \)** shifts the parent graph to the **right** by **1** unit.
4. **\( y = (x - 3)^2 \)** shifts the parent graph to the **right** by **3** units.

Would you like more details on why these transformations shift the graph in these ways or any other questions?

Here are 5 related questions to deepen your understanding:
1. How does the graph change if the transformation is \( y = (x + a)^2 \) with negative \( a \)?
2. What happens to the graph of \( y = x^2 \) if a vertical shift is applied, like \( y = x^2 + 2 \)?
3. How do horizontal shifts affect the vertex of a parabola?
4. How do transformations differ between horizontal and vertical shifts?
5. What does the graph look like if both a horizontal and vertical shift are applied, such as \( y = (x - 2)^2 + 3 \)?

**Tip**: For horizontal shifts, a positive value inside the parentheses shifts the graph left, while a negative value shifts it right!

y = (x + 1)^2 shifts the parent graph by ______ unit(s). y = (x + 3)^2 shifts the parent graph by ______ unit(s). y = (x - 1)^2 shifts the parent graph by ______ unit(s). y = (x - 3)^2 shifts the parent graph by ______ unit(s).

Understand how to find the horizontal shifts of the parabola y = x^2 using equations like y = (x + 1)^2 and y = (x - 3)^2. This problem demonstrates left and right shifts of parabolas, suitable for students in Grades 8-10.

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