Answer the questions below about the quadratic function. \[ f(x)=3 x^{2}-12 x+13 \] Does the function have a minimum or maximum value? Minimum Maximum What is the function's minimum or maximum value? Where does the mininsum or maximum value occur? \[ x= \] Continue

Step 1 ：The given function is a quadratic function of the form \(f(x) = ax^2 + bx + c\). The coefficient of \(x^2\) is positive, so the parabola opens upwards. This means the function has a minimum value.

Step 2 ：The minimum or maximum value of a quadratic function \(f(x) = ax^2 + bx + c\) occurs at \(x = -b/(2a)\).

Step 3 ：So, we need to calculate \(x = -b/(2a)\) and substitute this value into the function to find the minimum value.

Step 4 ：Given that a = 3, b = -12, c = 13, we find that the minimum value occurs at \(x = 2.0\).

Step 5 ：Substituting \(x = 2.0\) into the function, we find that the minimum value of the function is 1.0.

Step 6 ：Final Answer: The function has a minimum value. The minimum value of the function is \(\boxed{1}\) and it occurs at \(x = \boxed{2}\).