Complete the square to rewrite y = x2 + 6x + 2 in vertex form. Then state whether the vertex is a maximum or a minimum and give its coordinates.

Question

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Answer 1

Rewrite the original as:

y = x² + 6x +____ +2 - ____ (leaving a blank after the 1st two terms to complete the square)

Since the leading coefficient is 1, complete the square by taking 1/2 of b (which is 6) and squaring the result.

y = x² + 6x + 9 +2 - 9 (notice we had to add 9 to complete the square and subtract 9 to keep the equation in balance).

The whole point is that the 1st three terms now create a perfect square trinomial so can be written as a binomial squared.

y = (x + 3)² - 7 (this is called vertex form because it is easy to identify the vertex (-3, -7). The parabola opens upward because its leading coefficient is positive.

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