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The red graph is given as \( F(x) = x^2 \), which represents a standard parabola with its vertex at the origin (0, 0). The blue graph has the same shape as the red graph, which means it is also a parabola, but it is horizontally shifted.

Since the blue parabola is shifted to the left, its equation will take the form \( G(x) = (x - h)^2 \), where \( h \) is the horizontal shift of the vertex. By observing the graph, we see that the vertex of the blue parabola is at \( (-3, 0) \). Hence, the equation of the blue graph becomes:

\[
G(x) = (x + 3)^2
\]

This equation represents the same parabola as \( F(x) = x^2 \), but shifted 3 units to the left.

Would you like further details or have any questions?

Here are five related questions you might find helpful:
1. How do horizontal and vertical shifts affect the equation of a parabola?
2. What is the general form of a quadratic function?
3. How would the equation change if the blue graph was vertically shifted instead?
4. How can you find the vertex of a parabola from its equation?
5. What other transformations can be applied to parabolas?

**Tip:** When comparing the shapes of parabolas, focus on the vertex position and symmetry around the axis to determine any shifts or transformations.

The graphs below have the same shape. What is the equation of the blue graph?

Learn how to determine the equation of a horizontally shifted quadratic function. This problem involves understanding the basic properties of quadratic equations and graph transformations. Suitable for students in Grades 9-11.

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