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Cubic Graphs

Revise Cubic Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 10 flashcards. This topic appears less often, but it can still pick up marks when it appears in mixed-topic papers.

Study this topic

1

The Roller Coaster Curve

Introduction2

Cubic Graph Essentials

Key Facts3

Positive vs Negative Cubic Shapes

Diagram4

Key Features of Cubic Graphs

Deep Dive5

Drawing a Cubic Graph

Deep Dive6

Worked Example: Table of Values for y = x³ − 3x

Deep Dive7

Exam Tips for Cubic Graphs

Exam Tips8

Worked Examples

Notes9

Common Misconceptions

Misconceptions10

Topic Summary: Cubic Graphs

Summary

Sample Flashcards

How many roots can a cubic graph have?
A cubic graph can have 1, 2 or 3 roots (x-intercepts). - 3 distinct roots: crosses x-axis three times - 2 roots: touches at one point and crosses at another - 1 root: only crosses once (with a repeated root) Cubics ALWAYS have at least one real root.
What does the graph of y = x³ look like?
A smooth S-shaped curve. Key features: - Passes through the origin (0, 0) - Rises steeply for large positive x - Falls steeply for large negative x - Has a point of inflection at the origin (where it flattens then curves again)

Sample Questions

Which of the following best describes the general shape of the graph y = x³?

  • A. U-shape (parabola) opening upward
  • B. S-shaped curve rising from bottom-left to top-right
  • C. Horizontal straight line
  • D. S-shaped curve falling from top-left to bottom-right
1 markfoundation

Explain how you can tell from the equation of a cubic whether its graph rises or falls as x approaches positive infinity.

2 markshigher

11

exam-style questions

10

revision flashcards

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