f(x) = x² - 8x + 11
f(x) = (x²- 8x + ___) + 11
Take the middle term (-8), divide it by 2 the square it.
(-8/2)² = 16
Fill the ___ with 16. Also, subtract 16 outside the parentheses
f(x) = (x² - 8x + 16) + 11 - 16
f(x) = (x² - 8x + 16) - 5
Factor
f(x) = (x - 4)(x - 4) - 5
f(x) = (x - 4)² - 5 →→ vertex form
