hello everybody,

hope you've had an awesome holiday and happy new year!

i do not understand how this problem turns into\(f(x)=9(x-1/3)+2\)

here is the original thing:

\(f(x)=9x^2-6x+3\)

i got an answer that is totally off:

\(f(x)=9(x-1/3)^2+6\)

i don't understand where i went wrong, and every time i attempt to do the problem, i keep getting different results each time.

can someone please explain how and why this equals to \(f(x)=9(x-1/3)^2+2\)

thank you! <3

Nirvana Jan 3, 2020

#1**0 **

f(x) =9x^2-6x+3 'complete the square' to do this , leading coeff has to be 1

divide by 9 (we'll put it back in shortly)

f(x)/9 = x^2 - 2/3 x +1/3 now complete the square

x^2 - 2/3 x + 1/9 -1/9 +1/3

f(x) / 9 = (x-1/3)^2 - 1/9 + 3/9

f(x) / 9 = (x- 1/3)^2 + 2/9 Now remember that division by 9? Put the 9 back in by multiplying by 9

f(x) = 9 (x-1/3)^2 + 2 END !

ElectricPavlov Jan 3, 2020