f(x+1)=a(x+1)^2+b(x+1)+c=ax^2+2ax+a+bx+b+c=ax^2+x(2a+b)+a+b+c=x^2-3x+2
a=1;2a+b=-3; 2*1+b=-3;b=-5
a+b+c=2; 1-5+c=2; c=6
f(x)=ax^2+bx+c=x^2-5x+6
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f(x+1)=a(x+1)^2+b(x+1)+c=ax^2+2ax+a+bx+b+c=ax^2+x(2a+b)+a+b+c=x^2-3x+2
a=1;2a+b=-3; 2*1+b=-3;b=-5
a+b+c=2; 1-5+c=2; c=6
f(x)=ax^2+bx+c=x^2-5x+6