If $m$ and M respectively denote the minimum and maximum  of $f\left(x\right)=(x-1{)}^2+3$  for $x\in [-3,1]$ then the ordered pair $(m, M) =$

$f\left(x\right)=(x-1{)}^2+3\Rightarrow f(x)=2(x-1)$

$\Rightarrow f^{\mathrm{\prime }}\left(x\right)=2>0\Rightarrow f\left(x\right)=0\Rightarrow x=1$

Minimum value = 3

$-3\le x\le 1\Rightarrow -4\le x-1\le 0\Rightarrow (x-1{)}^2\le 16$

$\Rightarrow (x-1{)}^2+3\le 19$

Maximum value = 19 

 $\therefore (m,M)=(3,19)$