The concept of symmetry, taught from the lower secondary school, is one of the most important properties of quadratic functions. However, in mathematics textbooks, this symmetry is only briefly mentioned, and there is no content utilising this symmetry. In this session, we aim to address the process of transforming quadratic functions into factored forms and completing square forms using the symmetry through experimenting graph activities on the TI-Nspire CAS. Furthermore, determining the signs of coefficients from the graph of a given quadratic function is challenging mathematical reasoning for middle school students. This session seeks to address the process of easily inferring the signs of coefficients of a quadratic function graph by utilising linearity and polynomial properties of quadratic functions. Lastly, we aim to understand the Taylor series expansion process of a given function using the symmetry and linearity of quadratic functions through the TI-Nspire CAS.

Key takeaways:
1. Deriving factorisation and complete square form from the symmetry of quadratic function graphs.
2. Easily deducing the signs of coefficients from the given quadratic function graphs.
3. Understanding Taylor series expansion through experimenting quadratic function graphs using the TI Nspire CAS.