How do you complete the square for this:

Question

y= -1/3x^2 + 2x + 4

Answer 1

y = - ( 1 / 3 ) x² + 2 x + 4 =

- ( 1 / 3 ) ( x² - 6 x - 12 ) =

- ( 1 / 3 ) ( x² - 6 x + 9 - 21 ) =

- ( 1 / 3 ) [ ( x - 3 )² - 21 ] =

- ( 1 / 3 ) ∙ ( x - 3 )² - 21 ∙ ( - 1 / 3 ) =

- ( 1 / 3 ) ∙ ( x - 3 )² + 7

Remark:

( x - 3 )² =

x² - 2 ∙ x ∙ 3 + 3² =

x² - 6 ∙ x + 9

So:

x² - 6 x + 9 = ( x - 3 )²