MathDB
Parabolas

Source: IMC 2002 day 1 problem 1

October 7, 2005
conicsparabolaquadraticsalgebrapolynomialgeometrygeometric transformation

Problem Statement

A standard parabola is the graph of a quadratic polynomial y=x2+ax+by = x^2 + ax + b with leading co\"efficient 1. Three standard parabolas with vertices V1,V2,V3V1, V2, V3 intersect pairwise at points A1,A2,A3A1, A2, A3. Let A↦s(A)A \mapsto s(A) be the reflection of the plane with respect to the xx-axis. Prove that standard parabolas with vertices s(A1),s(A2),s(A3)s (A1), s (A2), s (A3) intersect pairwise at the points s(V1),s(V2),s(V3)s (V1), s (V2), s (V3).
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