Question

which equation is $y = -3x^2 - 12x - 2$ rewritten in vertex form? $y = -3(x - 2)^2 + 10$ $y = -3(x - 2)^2 - 2$ $y = -3(x + 2)^2 - 14$

Explanation:

Step1: Group x terms

$y = -3(x^2 + 4x) - 2$

Step2: Complete the square inside

$y = -3(x^2 + 4x + 4 - 4) - 2$

Step3: Rewrite as perfect square

$y = -3[(x+2)^2 - 4] - 2$

Step4: Distribute and simplify

$y = -3(x+2)^2 + 12 - 2$
$y = -3(x+2)^2 + 10$
(Note: The fourth option is cut off, but based on calculation, the correct vertex form is $y=-3(x+2)^2+10$; among the shown options, none match, but if we verify the given ones, the correct derived form is as above. Assuming the fourth option is $y=-3(x+2)^2+10$, that is the answer.)

Answer:

(Assuming the fourth option is) D. $y = -3(x + 2)^2 + 10$

(If the fourth option is not available, note that the calculated correct vertex form is $y=-3(x+2)^2+10$, which is the accurate rewrite of $y=-3x^2-12x-2$)