Answer:
y = 2 (x + 3)² − 4
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