Question

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

Answer 1

Answer:

Step-by-step 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

Answer:

f(x) = 2(x - 11)² - 57

Step-by-step 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