Let $ f_m: \mathbb R \to \mathbb R$, $ f_m(x)\equal{}(m^2\plus{}m\plus{}1)x^2\minus{}2(m^2\plus{}1)x\plus{}m^2\minus{}m\plus{}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.