This deep dive covers Key Features of Cubic Graphs within Cubic Graphs for GCSE Mathematics. 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 be a useful differentiator on mixed-topic papers. It is section 4 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 4 of 10
Practice
11 questions
Recall
10 flashcards
Key Features of Cubic Graphs
Roots (x-intercepts)
- 3 distinct roots: the curve crosses the x-axis three times
- 2 roots: the curve crosses at one point and TOUCHES (bounces off) at another — the touching point is a repeated root
- 1 root: the curve crosses once (a triple root or just one real root)
- A cubic ALWAYS has at least one real root
Turning Points
- A cubic can have 0 or 2 turning points — never exactly 1
- Local maximum: a peak where gradient goes from positive to negative
- Local minimum: a trough where gradient goes from negative to positive
- y = x³ has a point of inflection at the origin — momentarily flat but not a true turning point
Keep building this topic
Read this section alongside the surrounding pages in Cubic Graphs. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Cubic Graphs
Which of the following best describes the general shape of the graph y = x³?
Explain how you can tell from the equation of a cubic whether its graph rises or falls as x approaches positive infinity.
Quick Recall Flashcards
11 questions on Cubic Graphs — practise free
Instant marking, adaptive difficulty, and 10 spaced repetition flashcards. Free until your GCSEs.
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