Answer:
f(x) = (x -6)² +14
Explanation:
Completing the square involves writing part of the function as a perfect square trinomial.
Perfect square trinomial
The square of a binomial results in a perfect square trinomial:
(x -h)² = x² -2hx +h²
The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².
Completing the square
One way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.
Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...
f(x) = x² -12x +36 +50 -36
Rearranging into the desired form, this is ...
f(x) = (x -6)² +14
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Additional comment
Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.
f(x) = x² -12x +(36 +14)
f(x) = (x² -12x +36) +14
f(x) = (x -6)² +14