Given the function:

Let;s find the minimum or maximum value.
To determine if the function has a maximum or minimum, consider the following conditions:
• If the first term of the quadratic function is negative, the function has a maximum.
,
• If the first term of a quadratic function is positive, the function has a minimum.
Here, the first term is positive, therefore, the function has a minimum.
To find the minimum at x, apply the formula:

To determine the values of a and b, aply the general quadratic ecpression:

Now, compare both expressions:

Thus, we have:
a = 3
b = -12
c = 1
Hence, to find the minimum, substitute 3 for a, and -12 for b in the minimum formula above:

Now, to find the minimum, solve for f(2).
Substitute 2 for x in the function and evaluate for f(2):

Therefore, the minimum of the function occurs at the point: (2, -11)
When x = 2, y = -11
ANSWER:
Minimum; -11