The problem describes a quadratic function with a maximum value of $-3$ at $x = 8$.

Domain of a Quadratic Function:

The domain of any quadratic function is all real numbers since a parabola extends infinitely in both the positive and negative directions on the $x$-axis.

Therefore, the domain of the function is: $(-\infty, \infty)$

Would you like to explore the range or any further details?

Here are some related questions for further exploration:

1. What is the range of the given quadratic function?
2. How do you determine if a quadratic function opens upwards or downwards?
3. Can a quadratic function have more than one maximum or minimum point?
4. How does the vertex form of a quadratic function help in determining its properties?
5. What is the significance of the axis of symmetry in a quadratic function?

Tip: When dealing with quadratic functions, identifying the vertex can help quickly determine both the maximum or minimum value and the range.