What, exactly, did you do to find Q= (2x/3, 2y/3)? For that matter, what does it mean? Is the "y" in that given by y= 2x^2+ 3? If so, then (2x/3, 2y/3)= (2x/3, 4x^2/3+ 2). Now, let u= 2x/3 so that x= 3u/2. Putting that into y= 4x^2/3+ 2 gives y= 4(9u^2/4)+ 2= 9u^2+ 2 or (u, 9u^2+2). That gives y= 9x^2+ 2 as the locus.