Special case for deg(2/1) improper rational function:

𝐴=(𝑥,𝑓(𝑥))‖𝐼𝐴‖2=(𝑥−𝑥𝐼)2+(𝑓(𝑥)−𝑦𝐼)2

Sometimes you can use variable substitution to get sum of linear and reciprocal and then apply AM-GM inequality to solve for optimum.

References