y = x² - 12x + 8
First step is to move the 8 to the other side by subtract 8 from both sides. This gives you:
y - 8 = x² - 12x
Now we complete the square. Divide the b term (in this case 12) by 2, then square the result. You will then add that square to both sides. This gives you:
y - 8 + 36 = x² - 12x + 36
Combine like terms and factor:
y + 28 = (x - 6)²
y = (x - 6)² - 28. Option A should be your answer.
