Write y= 2x2 +12x+14 in vertex form.

y = 2 (x + 3)² − 4

Step-by-step explanation:

y = 2x² + 12x + 14

First, factor the leading coefficient from the first two terms:

y = 2 (x² + 6x) + 14

Complete the square.  Take half of 6, square it, then add and subtract.

(6/2)² = 3² = 9

y = 2 (x² + 6x + 9 − 9) + 14

Simplify:

y = 2 (x² + 6x + 9) − 2(9) + 14

y = 2 (x² + 6x + 9) − 18 + 14

y = 2 (x² + 6x + 9) − 4

Factor the perfect square.

y = 2 (x + 3)² − 4

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