Answer the questions below about the quadratic function.
$$f(x)=3x^2-12x+13$$
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 $f(x)=a{x}^2+bx+c$. 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 $f(x)=a{x}^2+bx+c$ 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 $\boxed{{\displaystyle 1}}$ and it occurs at $x=\boxed{{\displaystyle 2}}$.