Probably the easiest way to do this is to convert the given equation into "vertex form:
#color(white)("XXX")y=color(orange)(m)(x-color(red)(a))^2+color(blue)(b)# with vertex at #(color(red)(a),color(blue)(b))#
Given:
#color(white)("XXX")y=3x^2-2x-(3x+2)^2#
Expand and simplify the expression on the right side:
#color(white)("XXX")y=3x^2-2x-(9x^2+12x+4)#
#color(white)("XXX")y= -6x^2-14x-4#
Extract the #m# factor
#color(white)("XXX")y=color(orange)((-6))(x^2+14/6x)-4#
Complete the square
#color(white)("XXX")y=color(orange)((-6))(x^2+14/6x+14^2/12^2) - 4 +6*(14^2/(12^2))#
#color(white)("XXX")y=color(orange)((-6))(x+color(red)(14/12))^2 -4 +196/24#
#color(white)("XXX")y=color(orange)((-6))(x-color(red)((-7/6)))+color(blue)(25/6)#
graph{3x^2-2x-(3x+2)^2 [-3.342, 2.815, 2.025, 5.102]}
