$f(x)-2f(\frac{x}{2})+f(\frac{x}{4})=x^2$ , find $f(x)$ 
Find $f(x)$ if $f(x)-2f(\frac{x}{2})+f(\frac{x}{4})=x^2$, where $x, f(x)\in (-\infty , \infty)$ and $f(x)$ is continuous.


$y=mx^2+c$ is one solution  where $c\in R$
$$mx^2-2\cdot m \frac{x^2}{4}+m \frac{x^2}{16}=x^2$$
$$m=\frac{16}{9}$$
$$y=\frac{16}{9}x^2+c$$
As mentioned by @lulu if $f(x)$ is a solution than $f(x)+c$ is also a solution.  
