$f(x - 1) + f(x − 2) $ and the sum of coeficients If $f(x-1)+f(x-2) = 5x^2 - 2x + 9$
and
$f(x)= ax^2 + bx + c$
what would be the value of $a+b+c$?
I was doing
$f(x-1)+f(x-2)= f(x-3)$
then 
$f(x)$
a = 5
b = -2
c = 9

$(5-3)+(-2-3)+(9-3)$
But do not think is is correct
What would be correct approach?

We know $$f(x-1)=a(x-1)^2+b(x-1)+c\quad\text{and}\quad f(x-2)=a(x-2)^2+b(x-2)+c.$$ Expand these terms, add them, and combine like terms via powers of $x$. Now you can get three equations in three variables by equating the coefficients of the left with the right since you know $$f(x-1)+f(x-2)=5x^2-2x+9.$$
