Drag and drop the equation of the graph that is a reflection of this graph over the y-axis.
y = − (x +1)
2 or
y = − (x −1)
2 or
y = (−x −1)
2 or
y = (−x +1)
2

The equation of the graph that represents a reflection of \( y = -(x + 1)^2 \) over the **y-axis** can be found by replacing \( x \) with \( -x \) in the equation.

Starting with the original equation:
\[
y = -(x + 1)^2
\]

When reflected over the y-axis:
\[
y = -((-x) + 1)^2
\]

This simplifies to:
\[
y = -( -x + 1)^2
\]

Thus, the correct equation after reflection over the y-axis is:
\[
y = -( -x + 1)^2
\]

So, the corresponding equation is:
\[
\boxed{y = -( -x + 1)^2}
\]

Let me know if you'd like more details or have any questions!

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Here are 5 related questions to explore further:
1. What is the general rule for reflecting a graph over the y-axis?
2. How do transformations like shifts and reflections affect the vertex of a parabola?
3. What is the effect of reflecting a graph over the x-axis?
4. How can you determine the axis of symmetry for a quadratic function?
5. How does the graph of \( y = -(x + 1)^2 \) differ from \( y = (x + 1)^2 \)?

**Tip**: When reflecting a function over the y-axis, replace \( x \) with \( -x \) in the equation.

Drag and drop the equation of the graph that is a reflection of this graph over the y-axis. y = − (x +1)^2 or y = − (x −1)^2 or y = (−x −1)^2 or y = (−x +1)^2

Explore how to reflect the quadratic function y = -(x + 1)^2 over the y-axis. This math problem demonstrates key concepts in graph transformations, including reflections and symmetry. Ideal for students in Grades 9-11, with step-by-step guidance on applying reflection rules to quadratic functions.

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