Write this equation in the vertex form: y= -3x^+2x+1
by completing the square:
y = -3(x^2 - (2/3) + ... ) + 1
= -3(x^2 - (2/3)x + 1/9 - 1/9) + 1
= -3( (x - 1/3)^2 - 1/9) + 1
= -3(x - 1/3)^2 + 1/3 + 1
= -3(x - 1/3)^2 + 4/3
short-cut way:
the x of the vertex is -b/(2a) = -2/-6 = 1/3
then y = -3(1/9) + 2(1/3) + 1 = 4/3
so .... y = -3(x - 1/3)^2 + 4/3