Variation of Parameters in Quadratic Polynomials and Quadratic Sequences by Prof Helmer Aslaksen.

In this lecture, Prof. Aslaksen will explore two engaging and interconnected themes in school mathematics. The first focuses on using sliders in GeoGebra to investigate how quadratic polynomials behave as their coefficients vary—an approach that often leads to surprising insights. These observations will be explained both algebraically and geometrically.

The second part addresses a reverse question: Given a sequence of numbers, can we determine whether it forms a quadratic sequence? From there, we extend the same ideas to find sums of powers. These problems have a low entry point but offer rich opportunities for generalisation and mathematical reasoning, all within the realm of school mathematics.

This session is especially relevant for secondary school and junior college mathematics teachers seeking to deepen their students’ conceptual understanding through exploratory learning.