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} );

NiM+SSJmRzYiLCgqJEkieEdGJSIiIyMiIiQiIiVGKCMhI3AiIz8jIiNCRiwiIiI=

NiM+SSJGRzYiLDYiI0wiIiJJImFHRiUhJCc9SSJiR0YlISNlSSJjR0YlISNBKiRGKSIiIyIkYSQqJkYpRihGK0YoIiQrIyomRilGKEYtRigiI2cqJEYrRjAiI0kqJkYrRihGLUYoIiM/KiRGLUYwIiIl

NiM+SSRlcWFHNiIvLCohJCc9IiIiSSJhR0YlIiQzKEkiYkdGJSIkKyNJImNHRiUiI2ciIiE=

NiM+SSRlcWJHNiIvLCohI2UiIiJJImFHRiUiJCsjSSJiR0YlIiNnSSJjR0YlIiM/IiIh

NiM+SSRlcWNHNiIvLCohI0EiIiJJImFHRiUiI2dJImJHRiUiIz9JImNHRiUiIikiIiE=

NiM8JS9JImFHNiIjIiIkIiIlL0kiYkdGJiMhI3AiIz8vSSJjR0YmIyIjQkYp

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

display(dp, fp);

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