https://file.aiquickdraw.com/mathbot/file/17272007899510n52nz2j.jpg

The graph of \( F(x) \) shown in the image has the same basic parabolic shape as the function \( G(x) = x^2 \), but it appears shifted downward along the y-axis.

Let’s analyze the shifts:
- The graph looks like a vertical shift downward, as the vertex is at \( (0, -2) \) instead of \( (0, 0) \), which is where the vertex of \( G(x) = x^2 \) is located.

This suggests that the equation of \( F(x) \) is of the form:
\[
F(x) = x^2 - 2
\]
Thus, the correct answer is **D. \( F(x) = x^2 - 2 \)**.

Would you like further explanation on vertical shifts or anything else? Here are five related questions for deeper understanding:

1. What is the effect of adding a constant to a quadratic function?
2. How can you recognize vertical shifts in graphs?
3. How would a horizontal shift change the equation of a parabola?
4. What would the equation be if the graph was shifted upwards instead?
5. How would you determine if the parabola is reflected?

**Tip:** Always check the vertex of the graph to identify vertical shifts in quadratic functions.

The graph of F(x), shown below, has the same shape as the graph of G(x) = x^2. Which of the following is the equation of F(x)?

Explore how the quadratic function F(x) = x^2 - 2 represents a vertical shift downward of 2 units from the parent function G(x) = x^2. Understand vertical transformations and their effects on graphs, ideal for students in Grades 8-10.

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