Given the quadratic function \(f(x) = 3x^2 - 12x + 7\), find the maximum or minimum value of the function.

Step 1 ：To find the maximum or minimum of a quadratic function, we first need to identify whether the function opens upwards or downwards. Since the coefficient of \(x^2\) is positive, the function opens upwards and thus has a minimum value.

Step 2 ：The minimum or maximum value of a quadratic function \(f(x) = ax^2 + bx + c\) is given by the formula \(-\frac{b}{2a}\). Substituting the given values, we get \(-\frac{-12}{2\times3} = 2\).

Step 3 ：So, the minimum value of the function occurs at \(x = 2\). Now, we can find the minimum value by substitifying \(x = 2\) into the function: \(f(2) = 3(2)^2 - 12(2) + 7 = -1\).