Quadratic & Other Graphs - AQA GCSE Mathematics Revision

Topic overview

What you need to know

Quadratic & Other Graphs is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. The U-shaped (or inverted U-shaped) curve of a quadratic function y = ax² + bx + c. The maximum or minimum point of a parabola. Found by completing the square or using x = −b/(2a). A quadratic graph is symmetric about the vertical line x = −b/(2a), passing through the vertex.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

Parabola: The U-shaped (or inverted U-shaped) curve of a quadratic function y = ax² + bx + c.
Turning Point / Vertex: The maximum or minimum point of a parabola. Found by completing the square or using x = −b/(2a).
Line of Symmetry: A quadratic graph is symmetric about the vertical line x = −b/(2a), passing through the vertex.
Roots of a Quadratic Graph: The x-coordinates where the parabola crosses the x-axis (where y = 0).

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

Cubic Graph: A graph of y = ax³ + bx² + cx + d. It has an S-shape and can have up to 3 x-intercepts.
Reciprocal Graph: A graph of y = k/x. It has two separate curves (hyperbolas) in opposite quadrants and never touches the axes.
Exponential Graph: A graph of y = aˣ where a > 0. It curves steeply upward and has a horizontal asymptote at y = 0.
Asymptote: A line that a curve approaches but never actually reaches or crosses.

Core knowledge

Key facts for Quadratic & Other Graphs

8 essentials

Parabola

The U-shaped (or inverted U-shaped) curve of a quadratic function y = ax² + bx + c.

Turning Point / Vertex

The maximum or minimum point of a parabola. Found by completing the square or using x = −b/(2a).

Line of Symmetry

A quadratic graph is symmetric about the vertical line x = −b/(2a), passing through the vertex.

Roots of a Quadratic Graph

The x-coordinates where the parabola crosses the x-axis (where y = 0).

Cubic Graph

A graph of y = ax³ + bx² + cx + d. It has an S-shape and can have up to 3 x-intercepts.

Reciprocal Graph

A graph of y = k/x. It has two separate curves (hyperbolas) in opposite quadrants and never touches the axes.

Exponential Graph

A graph of y = aˣ where a > 0. It curves steeply upward and has a horizontal asymptote at y = 0.

Asymptote

A line that a curve approaches but never actually reaches or crosses.

Active recall

Close the notes and answer these

1.Without looking, explain parabola and give one example or consequence.
2.Without looking, explain turning point / vertex and give one example or consequence.
3.Without looking, explain line of symmetry and give one example or consequence.
4.Without looking, explain roots of a quadratic graph and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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