$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?

$$f''(x)=2a,  4a=f''(x-1)+f''(x-2)=10,  a=2.5$$
$$f'(x)=2ax+b=5x+b, 5(x-1)+5(x-2)+2b$$ 
$$f'(x-1)+f'(x-2)=10x-2, -15+2b=-2, b=6.5$$
$$f(x)=ax^2+bx+c, 2.5(x-1)^2+6.5(x-1)+2.5(x-2)^2+6.5(x-2)+2c=f(x-1)+f(x-2)=5x^2-2x+9$$
let $x=0$ on both side, $2.5-6.5+10-13+2c=9, c=8$
so $a+b+c=2.5+6.5+8=17$
