The problem is asking for the domain and range of a quadratic function, with the given information that the minimum value of the function is $-4$ at $x = 2$.

Domain:

The domain of a quadratic function, which is of the form $f(x) = ax^2 + bx + c$, is always all real numbers because quadratic functions are defined for every value of $x$. Therefore, the domain in interval notation is: $\boxed{(-\infty, \infty)}$

Range:

Since the quadratic function has a minimum value of $-4$ at $x = 2$, this means the parabola opens upwards (i.e., the coefficient of $x^2$ is positive). Therefore, the range is all values of $y$ greater than or equal to $-4$. The range in interval notation is: $\boxed{[-4, \infty)}$

Would you like more details on how the domain and range are derived or have any other questions?

Here are five related questions you might find helpful:

1. What is the general form of a quadratic function, and how can you determine its direction (upward or downward)?
2. How does the vertex of a quadratic function relate to its minimum or maximum value?
3. What is the difference between the domain and range of a function?
4. How can you find the vertex of a quadratic function from its equation?
5. Can the range of a quadratic function ever be all real numbers?

Tip: Always check the direction (upwards or downwards) of the parabola when determining the range of a quadratic function.