GlossariesGCSE GlossariesGCSE Maths GlossaryCubic Function

Cubic Function - GCSE Maths Definition

Reviewed by: Dan Finlay

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A cubic function is a polynomial function of degree three and can be expressed in the form:

f left parenthesis x right parenthesis equals a x cubed space plus b x squared space space plus c x plus d space

where:

  • a comma b comma c comma and d are constants,

  • 𝑎 space not equal to space 0 (to ensure the function remains cubic).

This function is called "cubic" because the highest power of x in a cubic function is 3, which means the graph of the function makes a curve with one or two bends. The shape of the graph can look like an "S" lying on its side or have one loop, and it can cross the x-axis up to three times, representing where the solution or "roots" of the equation are. Cubic functions are useful in GCSE Maths to understand how different types of curves behave and to solve real-world problems that involve changing rates or volumes.

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Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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