Question

To write f(x) = 2x2 – 44x + 185, factor out
from the first two terms.

Next, form a perfect square trinomial keeping the value of the function equivalent:

f(x) = 2(x2 – 22x + 121) + 185 – 242

The function written in vertex form is f(x) =
(x –
)2 +

Answer 1

f(x) = 2x² – 44x + 185

Take out common factor 2 from the first 2 terms:

f(x) = 2(x² – 22x) + 185

Add (b/2)² to form perfect square:

f(x) = 2 (x² - 22x + (22/2)² ) + 185 +  2 (22/2)²

Form perfect square:

f(x) = 2(x - 11 )² + 185 +  242

Combine common terms:

f(x) = 2(x - 11 )² + 427

Answer: f(x) = 2(x - 11 )² + 427