Question

1. convert to vertex form.

y = 2x² - 4x - 3

Explanation:

Step1: Factor out coefficient of $x^2$

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

Step2: Complete the square inside parentheses

$y = 2(x^2 - 2x + 1 - 1) - 3$

Step3: Rewrite as perfect square trinomial

$y = 2((x - 1)^2 - 1) - 3$

Step4: Distribute and simplify constants

$y = 2(x - 1)^2 - 2 - 3$
$y = 2(x - 1)^2 - 5$

Answer:

$y = 2(x - 1)^2 - 5$