Consider the quadratic equation y = 2x² − 2x. Complete the square to express the quadratic in standard form y = a(x − h)² + k. What are the values for a, h, and k?

Coefficient of $x$ is $-2$, half is $-1$, square is 1.

Add and subtract 1 inside:

$$y = 1 \cdot (x^2 - 2x + 1 - 1)$$ $$y = 1 \cdot ((x - 1)^2 - 1)$$

$$y = 1 \cdot (x - 1)^2 - 1 \cdot 1$$ $$y = (x - 1)^2 - 1$$

This is the vertex form $a(x - h)^2 + k$ where $a = 1$, $h = 1$, $k = -1$.

y = (x-1)^{2} - 1