Question

ing the square to write in vertex form
what is $f(x) = x^2 - 8x + 11$ written in vertex form?
$f(x) = (x + 4)^2 - 27$
$f(x) = (x + 4)^2 + 27$
$f(x) = (x - 4)^2 - 5$

Explanation:

Step1: Group x terms

$f(x) = (x^2 - 8x) + 11$

Step2: Complete the square

Take $\frac{-8}{2}=-4$, square it: $(-4)^2=16$. Add and subtract 16 inside the expression:
$f(x) = (x^2 - 8x + 16 - 16) + 11$

Step3: Rewrite as perfect square

$f(x) = (x - 4)^2 - 16 + 11$

Step4: Simplify constants

$f(x) = (x - 4)^2 - 5$

Answer:

$f(x) = (x - 4)^2 - 5$