f0[[Lambda]0_, y0_, y1_, x_, k_] :=-(-y0 + k*x*y1 + (1 - k*x^2)*[Lambda]1^2)^2 + 4*x^2*(1 - k^2*x)*[Lambda]1^2*Abs[-(k*y0) + y1 + k*[Lambda]1^2 - x*[Lambda]1^2]

f1[[Lambda]1_, y0_, y1_, x_, k_] := -(x*y0 - y1 + (1 - k*x^2)*[Lambda]1^2)^2 + 4*x^2*(-k + x)*[Lambda]1^2*Abs[-(k*y0) + y1 - [Lambda]1^2 + k^2*x*[Lambda]1^2]

f2[[Lambda]0_, [Lambda]1_, x_, k_] :=-1/27 + [Lambda]0^3 + 3*k*x*[Lambda]0^3 + 3*x*[Lambda]0^2*[Lambda]1 + [Lambda]1^3