IMC 2002 · Problem 1

A standard parabola is the graph of a quadratic polynomial $y = x^2 + ax + b$ with leading coefficient $1$. Three standard parabolas with vertices $V_1$, $V_2$, $V_3$ intersect pairwise at points $A_1$, $A_2$, $A_3$. Let $A \mapsto s(A)$ be the reflection of the plane with respect to the $x$ axis.

Prove that standard parabolas with vertices $s(A_1)$, $s(A_2)$, $s(A_3)$ intersect pairwise at the points $s(V_1)$, $s(V_2)$, $s(V_3)$.