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