Polynomials and power functions

Polynomials and power functions are the foundation for modelling non-linear relationships. Polynomial functions such as quadratic, cubic and quartic model variables raised to exponents of different degrees, while hyperbola and and truncus functions are power functions that involve variables raised to negative or fractional exponents.

These non-linear relationships are prevalent in real-world scenarios. For example, power functions can be used to describe gravitational forces in physics and population growth dynamics in biology; while polynomials can model demand-supply dynamics in economics and stress-strain relationships in engineering. Understanding these functions allows us to model and predict changes effectively. The properties and applications of quadratic, cubic, quartic, hyperbola, and truncus functions can give further insight into solving more complex problems.

This resource revises polynomials and power functions and within polynomials and power functions there are 3 key concepts:

• Quadratic Functions
• Cubic and Quartic Functions
• Hyperbola and Truncus Functions

To determine if this resource will benefit you, start by answering the following questions.

• How can complex relationships between variables be mathematically modelled?
• In what ways are these relationships represented visually on a graph?
• How can these models be adjusted to make them applicable across different contexts?

The answers to these questions are provided on the following pages. Use this resource to refresh your memory, reinforce your understanding of these concepts, and prepare more effectively for university-level learning.

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