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.