`y=-3(x-1)^2 + 3`

multiply `(x-1)^2`

`y=-3(x^2-2x+1)+3`

distribute -3

`y=-3x^2 + 6x - 3 + 3`

combine like terms, **answer** is:

`y=-3x^2+6x`

or **factored answer** is

`y=-3x(x-2)`

which makes **choice "d"** correct as both b and c work

`y=-3(x-1)^2 + 3`

multiply `(x-1)^2`

`y=-3(x^2-2x+1)+3`

distribute -3

`y=-3x^2 + 6x - 3 + 3`

combine like terms, **answer** is:

`y=-3x^2+6x`

or **factored answer** is

`y=-3x(x-2)`

which makes **choice "d"** correct as both b and c work