IMC 2002 Problem 1

A standard parabola is the graph of a quadratic polynomial $y = x^2 + ax + b$ with leading co"efficient 1. Three standard parabolas with vertices $V1, V2, V3$ intersect pairwise at points $A1, A2, A3$ . Let $A \mapsto s(A)$ be the reflection of the plane with respect to the $x$ -axis.

Prove that standard parabolas with vertices $s (A1), s (A2), s (A3)$ intersect pairwise at the points $s (V1), s (V2), s (V3)$ .