The graph of $f(x)=x^2$ is sketched in black and it had undergone a series of translations to graphs of functions $f_1$ sketched in green, $f_2$ sketched in blue, and $f_3$ sketched in red. $f\rightarrow f_1\rightarrow f_2\rightarrow f_3$. Use the translation rule and $f(x)=x^2$ to identify the function $f_1(x)$;

$f_1(x)=$

Use the translation rule and $f_1(x)$ to identify the function $f_2(x)$;

$f_2(x)=$

Use the translation rule and $f_2(x)$ to identify the function $f_3(x)$;

$f_3(x)=$