Plot3D[x^2+y^2,{x,-1,1},{y,-1,1},PlotStyle->Opacity[.2]]

Plot3D[x^2-y^2,{x,-1,1},{y,-1,1},PlotStyle->Opacity[.2]]

Plot3D[x y,{x,-3,3},{y,-3,3},PlotStyle->Opacity[.2]]

Show[Plot3D[((x )^2)+3x y +y^2,{x,-1/2,1/2},{y,-1,1},PlotStyle->Opacity[.2],BoxRatios->Automatic,PlotRange->{-.5,1}],ParametricPlot3D[{x,x,4x^2},{x,-1/2,1/2},PlotStyle->{Thick,Red}],ParametricPlot3D[{x,-x,-x^2},{x,-1/2,1/2},PlotStyle->{Thick,Red}],ParametricPlot3D[{x,0,x^2},{x,-1/2,1/2},PlotStyle->Thick],ParametricPlot3D[{0,y,y^2},{y,-1/2,1/2},PlotStyle->Thick]]

Graphics3D[{Black,Sphere[{0,0,1},.05],Sphere[{4/3,4/3,59/27},.05]}];
Plot3D[-x^3+4 x y-2y^2+1,{x,-1,2},{y,-1,2},PlotRange->{.5,2.5}];
Show[%,%%]

Graphics3D[{Black,Sphere[{0,0,0},.05],Sphere[{0,1/√2,-1/4},.05],Sphere[{0,-1/√2,-1/4},.05]}];
Plot3D[x^2-y^2+y^4+x^2 y^2,{x,-1,1},{y,-1,1},PlotRange->{-.5,.5}];
Show[%,%%]