Question

f(x)= -x^2 +6x -5
complete the square

Answer 1

f(x)= -x^2 +6x -5
= -1(x^2 - 6x - 5)
take 1/2 of the -6, then square it: -----> 9
= -(x^2 - 6x + 9 - 9-5)
= -( (x-3)^2 - 14)
= .....

Answer 2

Reiny's solution is incorrect.

- ( ( x - 3 )² - 14 ) = - ( x² - 2 ∙ x ∙ 3 + 3² - 14 ) =

- ( x² - 6 x + 9 - 14 ) = - ( x² - 6 x - 5 ) = - x² + 6 x + 5


but

- x² + 6 x - 5 = - x² + 6 x - 9 + 4 = ( - x² + 6 x - 9 ) + 4 =

- ( x² - 6 x + 9 ) + 4 = - ( x - 3 )² + 4 = - [ ( x - 3 )² - 4 ]

So:

- x² + 6 x - 5 = - [ ( x - 3 )² - 4 ]

Answer 3

Bosnian is correct, my second line should be
= <b>-1(x^2 - 6x + 5)</b> instead of = -1(x^2 - 6x - 5)