SeedRandom[1];
s:=RandomReal[NormalDistribution[0,1]];
f1[x_]:=(x^2)+3x+6+s;
body=Table[{x,f1[x]},{x,-2,3,0.2}];
pl1=ListPlot[body,AxesLabel->{"x","f[x]"},PlotStyle->{Red,PointSize[0.02]}];

vysledek
Fit[body,{1,x,(x^2)},x]

odchylka[{x_,f_}]:=(((a*(x^2)+b*x+c-f))^2);
sumerr=Simplify[Plus@@(odchylka/@body)];
dosabc=Solve[{D[sumerr,a]==0,D[sumerr,b]==0,D[sumerr,c]==0}][[1]];
vysledek=a*(x^2)+b*x+c/.dosabc;
pl2=Plot[vysledek,{x,-2,3},PlotStyle->Thickness[0.006]];
Show[pl1,pl2]