f[x_,r_]:=r x+x^3-x^5;GraphicsGrid[{{Plot[f[x,-1/2],{x,-1,1}],Plot[f[x,-1/8],{x,-1,1}],Plot[f[x,1],{x,-2,2}]}}]

Clear[r]
xstar1=-Sqrt[(1+Sqrt[1+4r])/2];
xstar2=-Sqrt[(1-Sqrt[1+4r])/2];
xstar3=0;
xstar4=Sqrt[(1-Sqrt[1+4r])/2];
xstar5=Sqrt[(1+Sqrt[1+4r])/2];

largeampl=Plot[{xstar1,xstar5},{r,-1/4,1},PlotStyle->{{Black,Thickness[.01]},{Black,Thickness[.01]}},AspectRatio->1,AxesLabel->{"r","(SuperStar[x])"},LabelStyle->Directive[24]]

smallampl=Plot[{xstar2,xstar4},{r,-1/4,0},PlotStyle->{{Blue,Dashing[{0.02,0.02}],Thickness[.01]},{Blue,Dashing[{0.02,0.02}],Thickness[.01]}},AspectRatio->1,AxesLabel->{"r","(SuperStar[x])"},LabelStyle->Directive[24]]

zerostable=Plot[0,{r,-1,0},PlotStyle->{Black,Thickness[.01]},AspectRatio->1,AxesLabel->{"r","(SuperStar[x])"},LabelStyle->Directive[24]];

zerounstable=Plot[0,{r,0,1},PlotStyle->{Blue,Dashing[{0.02,0.02}],Thickness[.01]},AspectRatio->1,AxesLabel->{"r","(SuperStar[x])"},LabelStyle->Directive[24]];

Show[largeampl,smallampl,zerostable,zerounstable,PlotRange->All]