The graph you provided shows a parabola, which is based on the function $y = x^2$. The problem asks to describe the transformation applied to this function.

From the image:

• The vertex of the original function $y = x^2$ is at $(0, 0)$.
• The graph has been shifted upward so that the vertex is now at $(0, 5)$.

Transformation:

A vertical shift upward by 5 units modifies the function as follows: $f(x) = x^2 + 5$

This describes the graph.

Would you like a detailed explanation of vertical shifts or have any questions?

Related Questions:

1. What is the effect of shifting a parabola downward on its equation?
2. How would the graph look if the transformation was $f(x) = x^2 - 5$?
3. Can you describe how horizontal shifts affect the equation $y = x^2$?
4. How would a transformation like $f(x) = 2x^2$ stretch or compress the parabola?
5. What happens to the vertex of $y = x^2$ if we add a constant $k$?

Tip:

When analyzing transformations, focus on the vertex and note any vertical or horizontal shifts, stretches, or reflections.