This is Chapter 2 – Quadratics for the Year 11 Mathematical Methods course.

Quadratic functions are one of the most important algebraic structures students encounter in senior mathematics. They appear repeatedly in modelling contexts involving motion, optimisation, and curved behaviour. This chapter develops both procedural fluency and deeper conceptual understanding of parabolic functions.

Students begin by solving quadratic equations using factorisation and formula-based approaches. The discriminant is introduced as a structural tool that reveals the nature of solutions before full calculation is even completed. Exploring the sum and product of roots strengthens algebraic reasoning and connects symbolic manipulation with graphical interpretation.

Graphical analysis then becomes central. Students interpret intercepts, turning points, and axis of symmetry while learning to determine equations from graphical information. Problem-solving and optimisation tasks require students to model realistic situations carefully and justify their reasoning clearly.

Quadratic modelling is foundational in physics (projectile motion), economics (revenue and profit curves), and engineering design. Developing confidence here opens pathways into STEM disciplines that rely on curved modelling and optimisation analysis.

Subchapters:

• 2A: Solving quadratic equations
• 2B: The discriminant of a quadratic
• 2C: The sum and product of the roots
• 2D: Quadratic functions
• 2E: Finding a quadratic from its graph
• 2F: Where functions meet
• 2G: Problem solving with quadratics
• 2H: Quadratic optimisation

By the end of this chapter, students will analyse and apply quadratic models with confidence, precision, and strong conceptual understanding.