What is the equation of the axis of symmetry of the graph of y + 3x - 6 = - 3 (x - 2) 2 + 4?

Convert to y=ax^2+bx+c form

y+3x-6=-3 (x-2) ^2+4

exponent

y+3x-6=-3 (x^2-4x+4) + 4

distribute

y+3x-6=-3x^2+12x-12+4

minus 3x both sides

y-6=-3x^2+9x-8

add 6 both sides

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

in form ax^2+bx+c=y

x coordinate of the vertex=-b/2a

and the axis of symmetry is the x coordianat

a=-3

b=9

-9 / (2*-3) = - 9/-6=3/2

x=3/2 is axis of symmetry