which equation is y = -3x² - 12x - 2 rewritten in vertex form?\no y = -3(x + 2)² + 10\no y = -3(x - 2)² +…

Explanation:

Step1: Factor out -3 from first two terms

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

Step2: Complete the square inside the parentheses

For $x^{2}+4x$, half of 4 is 2 and $2^{2} = 4$. So we add and subtract 4 inside the parentheses: $y=-3(x^{2}+4x + 4-4)-2$

Step3: Rewrite the expression

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

Step4: Distribute -3

$y=-3(x + 2)^{2}+12-2$

Step5: Simplify

$y=-3(x + 2)^{2}+10$

Answer:

$y=-3(x + 2)^{2}+10$ (the first option)