What is f (x) = x2 - 8x + 11 written in vertex form

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