Question

Write f(x) = 2x2 – 44x + 185 in vertex form.

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

Explanation:

`f(x)=2x^2-44x+185\\\\=2(x^2-2*11*x)+185\\\\=2(x^2-2*11*x+11^2)+185-2*121\\\\\boxed{f(x)=2(x-11)^2-57}\\\\vertex\ is\ (11,-57)`

Answer 2

f(x) = 2(x - 11)² - 57

Explanation:

Given

f(x) = 2x² - 44x + 185 ( factor out 2 from the first two terms )

f(x) = 2(x² - 22x) + 185

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² - 22x

f(x) = 2(x² + 2(- 11)x + 121 - 121 ) + 185

= 2(x - 11)² + 2(- 121) + 185

= 2(x - 11)² - 242 + 185

f(x) = 2(x - 11)² - 57 ← in vertex form