12. If the quadratic functions $f_{1}(x)=a_{1} x^{2}+b_{1} x+c_{1}$ and $f_{2}(x)=a_{2} x^{2}+b_{2} x+c_{2}$, such that $f_{1}(x)-f_{2}(x)$ is a monotonically decreasing function on $[1,2]$, and has a maximum value of 5 and a minimum value of 3 on $[1,2]$, please provide a set of functions that satisfy the above conditions: $f_{1}(x)=$ $\qquad$ , $f_{2}(x)=$ $\qquad$
12. $f_{1}(x)=x^{2}+x+5, f_{2}(x)=x^{2}+3 x-2$ (the answer is not unique).
$f_{1}(x)-f_{2}(x)=k x+m$, given that the maximum value of $f(x)$ on $[1, 2]$ is 5 and the minimum value is 3, then $\left\{\begin{array}{l}k+m=5 \\ 2 k+m=3,\end{array}\right.$ we get $\left\{\begin{array}{l}k=-2 \\ m=7,\end{array}\right.$ which means $f_{1}(x)-f_{2}(x)=-2 x+7$.