which equation is y = 6x² + 12x - 10 rewritten in vertex form?\no y = 6(x + 1)² - 11\no y = 6(x + 1)²…

Explanation:

Step1: Factor out the coefficient of $x^{2}$

$y = 6x^{2}+12x - 10=6(x^{2}+2x)-10$

Step2: Complete the square inside the parentheses

For the quadratic expression $x^{2}+2x$, we know that $(x + a)^{2}=x^{2}+2ax+a^{2}$. Here $2a = 2$, so $a = 1$ and $x^{2}+2x=(x + 1)^{2}-1$. Then $y=6((x + 1)^{2}-1)-10$.

Step3: Expand and simplify

$y=6(x + 1)^{2}-6-10=6(x + 1)^{2}-16$

Answer:

$y = 6(x + 1)^{2}-16$ (corresponding to the last - option)