https://file.aiquickdraw.com/mathbot/file/1725974175878a7wrwdgz.jpg

The given graph represents a transformation of the function \( y = x^2 \). To determine the equation of the transformed function, let's analyze the graph.

### Key observations:
1. The vertex of the original function \( y = x^2 \) is at the point (0, 0), but in the transformed graph, the vertex has shifted to (0, -1).
2. The graph maintains its parabolic shape, so there is no horizontal or vertical stretch/compression.
3. The graph has been shifted **down** by 1 unit.

### Transformation:
The function \( y = x^2 \) has been vertically shifted downward by 1 unit, which gives us the transformation:
\[
y = x^2 - 1
\]

### Final equation:
The equation for the function graphed above is:
\[
y = x^2 - 1
\]

Would you like more details on transformations or have any questions?

### Related Questions:
1. How do you identify vertical or horizontal shifts from a graph?
2. What effect does adding or subtracting a constant from \( x^2 \) have on the graph?
3. How do you recognize a vertical stretch or compression in a transformed graph?
4. How do you determine if a parabola has been reflected over the x-axis?
5. What is the significance of the vertex in quadratic functions?

### Tip:
Always examine the vertex and general shape of the graph to quickly identify transformations.

The graph above is a transformation of the function x^2. Write an equation for the function graphed above.

This problem explains how to find the equation of a quadratic function from its graph. Learn how to identify transformations like vertical shifts and apply them to y = x^2, with the final equation being y = x^2 - 1. Suitable for students in Grades 8-10.

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