Fiducia TogetherQuadratic equation
An equation with an x² term. Three ways to solve one, and knowing which is the exam skill.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
A quadratic has the form ax² + bx + c = 0. It normally has two solutions, sometimes one, sometimes none in real numbers.
Where it applies
Both tiers; the formula and completing the square are Higher.
How it works
Three methods. Factorising is fastest when it works. The quadratic formula always works and is given on some papers and not others. Completing the square rewrites it as (x + p)² + q, which also gives the turning point of the graph.
The discriminant b² − 4ac tells you how many solutions there are before you find them.
How to use it in your work
Try factorising first; go to the formula when it does not factorise quickly.
If the question asks for exact answers, leave surds as surds.
"Completing the square" questions are usually really about the turning point — read what is being asked for.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.