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Mathematics
24 February, 00:07
Write y = 2x2 + 12x+14 in vertex form.
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Scott Ferguson
24 February, 00:36
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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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