feb20-maple.mw

> restart:with(plots):

Warning, the name changecoords has been redefined

> data:= [ [1,3], [2,2], [3,2], [4,4] ]:
f:= 3/4*x^2 - 69/20*x + 23/4;
g:= x->a*x^2+b*x+c:
F:= simplify(
        ( g(data[1][1]) - data[1][2] )^2 +
        ( g(data[2][1]) - data[2][2] )^2 +
        ( g(data[3][1]) - data[3][2] )^2 +
        ( g(data[4][1]) - data[4][2] )^2
        );
eqa:= simplify(diff(F,a))=0;
eqb:= simplify(diff(F,b))=0;
eqc:= simplify(diff(F,c))=0;
solve( {eqa, eqb, eqc}, {a,b,c} );

f := 3/4*x^2-69/20*x+23/4

F := 33-186*a-58*b-22*c+354*a^2+200*a*b+60*a*c+30*b^2+20*b*c+4*c^2

eqa := -186+708*a+200*b+60*c = 0

eqb := -58+200*a+60*b+20*c = 0

eqc := -22+60*a+20*b+8*c = 0

{a = 3/4, b = (-69)/20, c = 23/4}

> dp:= pointplot(data, symbol=CIRCLE, symbolsize=15):
fp:= plot(f, x=0..5):

> display(dp, fp);

[Plot]

>

>