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This topic studies quadratic functions and their parabola graphs, and uses the discriminant b² − 4ac to determine the number and nature of the roots without solving the equation. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
The discriminant is b squared minus 4ac. Positive gives two distinct roots, zero gives one repeated root, negative gives none. Set the equation to zero before reading off a, b and c — that is the step people skip.
Before you start
Everything here rests on solving quadratics. It is Pure 1 content. It then feeds into the number of roots and curve sketching. The topic sits within Algebra.
What you learn
The hard exam marks come from turning a worded condition (‘equal roots’, ‘two distinct points’, ‘a tangent’, ‘for all values’) into a discriminant statement and solving it — often a quadratic inequality in an unknown. To find where a line meets a curve, substitute and form a quadratic. The course works through the discriminant & nature of roots, conditions on an unknown, the discriminant & the graph, tangency & intersection with a line and ‘Show that’ & range of values. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Quadratic Functions & Discriminant as one of the Algebra topics in our A-level course library, at the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Students often pair it with Solving Quadratics, Transformations of Graphs and Algebraic Division. You can drill this strand further on the Algebra revision engine, with your accuracy saved to your skill tree.
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