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

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



To write f(x) = 2x2 – 44x + 185, factor out
2
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) =
2
(x –
11
)2 +
-57
.

Answer 2

f(x) = 2(x-11)^2 - 57

Explanation:

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

Next, form a perfect square tri nomial keeping the value of the function equivalent: f(x) = 2(x^2 – 22x + 121) + 185 – 242

To get vertex form we factor x^2 -22x+121

product is 121 and sum is -22

-11*-11= 121 and sum -11+(-11)= -22

x^2 -22x+121

(x-11)(x-11)

f(x) = 2(x^2 – 22x + 121) + 185 – 242

f(x) = 2(x-11)(x-11)+ 185 – 242

f(x) = 2(x-11)^2 - 57