Answer:

y = x²- 4x + 1

= ( x² - 4 + (4/2)² ) + 1 /add (4/2)² = 4 to make it a perfect square trinomial

the new expression is (x²-4x + 4) - 4 + 1 / since we have added 4

we must also - 4 to balance up

= (x-2)² -3 / ( x²-4x + 4) = (x-2)²

= 1(x-2)² -3 / vertex form a(x-h)² + k