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.