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?

Step 1: Start with the given quadratic expression.

$y = x^2 - 2x$

Step 2: Factor out the leading coefficient $a = 1$ from the $x^2$ and $x$ terms (not necessary here but general form).

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

Step 3: Complete the square inside the parentheses. Coefficient of $x$ is $-2$, half is $-1$, square is $1$.

Add and subtract $1$ inside:

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

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

Step 4: Distribute the leading coefficient.

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

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

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

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