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To determine the range of the quadratic function given in the graph, we first need to identify the lowest point (vertex) of the parabola since it opens upwards.

### Analyzing the Graph

1. **Shape of the Parabola**: The graph shows a parabola that opens upwards.
2. **Vertex**: The vertex of the parabola is at the point \((x, y) = (0, -6)\).
3. **Direction**: Since the parabola opens upwards, the range of the quadratic function will start from the y-coordinate of the vertex and extend to positive infinity.

### Range of the Function

Since the lowest point of the parabola is at \(y = -6\) and the parabola extends upwards, the range of the function is all \(y\) values greater than or equal to \(-6\).

### Conclusion

The correct range of the quadratic function is:

\[
\{y \mid y \geq -6\}
\]

**Answer:** Option 2: \(\{y \mid y \geq -6\}\).

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### Related Questions:
1. What is the domain of this quadratic function?
2. How do we find the vertex of a quadratic function algebraically?
3. What determines whether a parabola opens upwards or downwards?
4. How does the coefficient of \(x^2\) affect the width of the parabola?
5. How do we find the x-intercepts of a quadratic function?

**Tip:** When analyzing the range of a function, always look for the vertex and direction (up or down) of a parabola.

What is the range of this quadratic function?

Learn how to determine the range of a quadratic function by analyzing the graph of a parabola. This problem involves identifying the vertex and understanding the direction of the parabola. Suitable for students in Grades 9-12.

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