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The problem asks for the equation of the function \( g(x) \), which has the same shape as the given function \( f(x) = x^2 \) but is shifted up by 3 units.

To find the equation of \( g(x) \), we start with the base function \( f(x) = x^2 \). When a function is shifted vertically by 3 units, we add 3 to the function:

\[
g(x) = f(x) + 3
\]

Since \( f(x) = x^2 \), we substitute this into the equation:

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

Thus, the equation for \( g(x) \) is:

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

Would you like further details or have any questions?

Here are 5 related questions:
1. What would happen if the function was shifted down by 3 units?
2. How does shifting horizontally affect the function equation?
3. What does the vertex of the parabola represent after the vertical shift?
4. Can you describe how the graph of \( g(x) = x^2 + 3 \) differs from \( f(x) = x^2 \)?
5. How would you shift the function to the left or right?

**Tip:** When graphing, vertical shifts affect the \( y \)-coordinates, while horizontal shifts modify the \( x \)-coordinates.

The graph of f(x) = x^2 is shown below. Sketch the graph of a function g(x) that has the same shape as f(x) but shifted up 3 spaces. Now write the equation for g(x).

Learn how to graph a vertically shifted quadratic function. Starting with f(x) = x^2, this problem shifts the function up by 3 units to create g(x) = x^2 + 3. Understand how vertical transformations affect the shape and position of the parabola.

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