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.