Consider the function $f(x) = 3x^2 - 12x - 6$.
a. Determine, without graphing, whether the function has a minimum value or a maximum value.
b. Find the minimum or maximum value and determine where it occurs.
c. Identify the function's domain and its range.
a. The function has a \boxed{} value.
b. The minimum/maximum value is \boxed{} It occurs at $x = \boxed{}$
c. The domain of $f$ is \boxed{} (Type your answer in interval notation.)
The range of $f$ is \boxed{} (Type your answer in interval notation.)