MathDB

Given are

n

points with different abscissas in the plane. Through every pair points is drawn a parabola - a graph of a square trinomial with leading coefficient equal to

1

. A parabola is called

good

if there are no other marked points on it, except for the two through which it is drawn, and there are no marked points above it (i.e. inside it). What is the greatest number of

good

parabolas?

Problem Statement