a=-1;
b=2;
g[x_]=(x^2);
h[x_]=g[a]+((g[b]-g[a])/(b-a))(x-a);
f[x_]=g[x]-h[x];
TANGENT[x_]=g[(1/2)]+((g[b]-g[a])/(b-a))(x-(1/2));
P0=Plot[{g[x]},{x,-1.5,3},PlotRange->{-3,5}];
P1=Plot[{g[x],h[x]},{x,-1.5,3},PlotRange->{-3,5},PlotStyle->{Automatic,Dashing[Large]}];
P2=Plot[f[x],{x,-3,3},PlotRange->{-3,5}];
P3=Plot[{f[x],-2.25},{x,-3,3},PlotRange->{-3,5}];
P4=Plot[{g[x],h[x],TANGENT[x]},{x,-1.5,3},PlotRange->{-3,5},PlotStyle->{Automatic,Dashing[Large]}];

Manipulate[Which[
n==0,
Show[{P0,Graphics[{Disk[{a,g[a]},.05],Disk[{b,g[b]},.05]}]},AspectRatio->1],
n==1,
Show[{P1,Graphics[{Disk[{a,g[a]},.05],Disk[{b,g[b]},.05]}]},AspectRatio->1],
n==2,
Show[{P2,Graphics[{Disk[{a,0},.07],Disk[{b,0},.07]}]},AspectRatio->1],
n==3,
Show[{P3,Graphics[{Disk[{a,0},.05],Disk[{b,0},.05]}]},AspectRatio->1],
n==4,
Show[{P4,Graphics[{Disk[{a,g[a]},.05],Disk[{b,g[b]},.05]}]},AspectRatio->1]
],

{n,0,4,1}]