f[x_]=Sin[x^2]/x; 
g[x_] = x;
Plot[{f[x],g[x]},{x,0,1},PlotStyle->{Red,Blue}]

A={{(1-.8)^2,(1-.8)},{(.6-.8)^2, (.6-.8)}}

coefs=LinearSolve[A,{f[1.0]-f[.8],f[.6]-f[.8]}]

h[x_]=coefs.{(x-.8)^2,(x-.8)}+f[.8]

Plot[{f[x],h[x]},{x,0,1},PlotStyle->{Red,Blue}]