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Orlov [11]
2 years ago
8

Rewrite the function by completing the square.

Mathematics
1 answer:
ddd [48]2 years ago
6 0

Answer:

  f(x) = (x -6)² +14

Step-by-step explanation:

Completing the square involves writing part of the function as a perfect square trinomial.

<h3>Perfect square trinomial</h3>

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.

<h3>Completing the square</h3>

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

__

<em>Additional comment</em>

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

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