The domain of the function appears to be all numerical values, as there are no specific restrictions mentioned. However, based on the experiments, there seems to be an interval where the function displays unexpected behavior. This interval is between -32 and 32, where the function outputs negative values, and the output values increase as we move towards the boundaries of this interval.

[CODE]:

```python
def f(x):
    a = -0.01  # coefficient of x^2
    b = 2      # coefficient of x
    c = -2.5   # constant term
    return a*x**2 + b*x + c
```

Note: The specific values of the coefficients may vary, but this code provides an approximation of the behavior of the function based on the given experiments.