MD-MO 2008 Problem 1

Let $f_m: \mathbb R \to \mathbb R$ , $f_m(x)=(m^2+m+1)x^2-2(m^2+1)x+m^2-m+1,$ where $m \in \mathbb R$ .

1. Find the fixed common point of all this parabolas.

2. Find $m$ such that the distance from that fixed point to $Oy$ is minimal.