which equation is y = 2x² - 8x + 9 rewritten in vertex form?\no y = 2(x - 2)² + 9\no y = 2(x - 2)² + 5\no y…

Explanation:

Step1: Factor out the coefficient of $x^{2}$ from the first - two terms

$y = 2x^{2}-8x + 9=2(x^{2}-4x)+9$

Step2: Complete the square inside the parentheses

For the quadratic expression $x^{2}-4x$, we know that $(x - a)^2=x^{2}-2ax + a^{2}$. Here, $-2a=-4$, so $a = 2$ and $x^{2}-4x=(x - 2)^{2}-4$. Then $y=2((x - 2)^{2}-4)+9$.

Step3: Expand and simplify

$y=2(x - 2)^{2}-8 + 9=2(x - 2)^{2}+1$

Answer:

$y = 2(x - 2)^{2}+1$ (the third option)