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!