Question

How do you complete the square for `y= -3x^2+12x+9`?

Answer 1

`y = -3x^2+12x+9`

`= -3(x^2-4x-3)`

`= -3((x^2-4x+4)-4-3)`

`= -3((x-2)^2 - 7)`

In general:
`ax^2+bx+c = a(x+b/(2a))^2 + (c-b^2/(4a))`

Answer 2

`y = -3x^2 + 12x + 9 = -3(x^2 - 4x - 3)`=

`= -3(x^2 - 4x + 4 - 4 - 3) = -3(x - 2)^2 + 21`

`(x - 2)^2 = -21/-3 = 7`

`x - 2 = sqrt7 -> x = 2 + sqrt7`

`x - 2 = -sqrt7 -> x = 2 - sqrt7`