$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?

$$f(x-1)+f(x-2) = 5x^2 - 2x + 9$$and $$f(x)=ax^2+bx+c$$
for $x=1,2,3$ we get the system
$$f(0)+f(-1)=a-b+2c =12$$
$$f(1)+f(0)=a+b+2c=25$$
$$f(2)+f(1)=5a+3b+2c = 48$$
with solutions 
$$a=5/2,b=13/2,c=8$$
so $$f(x)=\frac{5}{2}x^2+\frac{13}{2}x+8$$
