https://file.aiquickdraw.com/mathbot/file/1729634545932plnviqhd.jpg

The graph shown is a parabola opening upwards, indicating that it represents a quadratic function. The range of a quadratic function depends on the vertex, which represents the minimum or maximum point. 

In this case, the vertex of the parabola is at the point \((3, -9)\), which is the minimum point since the parabola opens upwards. This means the function takes values starting from \(-9\) and increases to positive infinity.

Thus, the **range** of this quadratic function is:

\[
\boxed{[-9, \infty)}
\]

Would you like a detailed explanation of why the range is determined this way or have any questions?

Here are 5 related questions:
1. How do you find the vertex of a quadratic function algebraically?
2. What is the domain of a quadratic function?
3. How do you know if a parabola opens upwards or downwards?
4. Can the range of a quadratic function ever be all real numbers?
5. How does the axis of symmetry relate to the vertex of a parabola?

**Tip**: For quadratic functions in standard form \(y = ax^2 + bx + c\), the sign of \(a\) determines if the parabola opens upwards (\(a > 0\)) or downwards (\(a < 0\)).

What is the range of this quadratic function?

This page explains how to find the range of a quadratic function with a vertex at (3, -9). The parabola opens upwards, making the range [-9, infinity). Suitable for students in Grades 8-10.

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