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The graph provided is a vertical shift of the standard parabola \( y = x^2 \). The graph looks like the function has been shifted upward by 2 units. This is because the vertex of the standard parabola \( y = x^2 \) is at \( (0, 0) \), but in the given graph, the vertex appears to be at \( (0, 2) \).

So, the equation for the function \( g(x) \) would be:

\[
g(x) = x^2 + 2
\]

This represents the parabola shifted vertically by 2 units. 

Would you like further details or clarifications?

Here are 5 related questions for further understanding:
1. How would the formula change if the graph was shifted downward?
2. What is the effect of a horizontal shift on the equation of a parabola?
3. How would you shift the graph of \( y = x^2 \) to the left by 3 units?
4. What happens to the graph if both horizontal and vertical shifts are applied simultaneously?
5. Can you explain how a reflection across the x-axis would affect the equation?

**Tip**: When dealing with shifts in a graph, remember that vertical shifts modify the constant (outside the function), while horizontal shifts affect the variable inside the function.

The graph in the figure is a horizontal and/or vertical shift of the graph of y = x^2. Find a formula for the function graphed in the figure.

Solve a quadratic function problem involving vertical shifts by determining the function g(x) for the parabola graph shown. This problem highlights key algebra concepts and graph transformations for high school students.

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