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 ($a < 0$).