GraphsIntroduction

The Roller Coaster Curve

Part of Cubic Graphs · GCSE GCSE Mathematics revision

This introduction covers The Roller Coaster Curve 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 1 of 10 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 10

Practice

11 questions

Recall

10 flashcards

The Roller Coaster Curve

A roller coaster rises, reaches a peak, descends into a valley, then climbs again before plummeting off the end. That distinctive shape — a hill followed by a valley — is exactly what many cubic graphs look like. Unlike the simple U-shape of a quadratic, a cubic curve can change direction twice, cross the x-axis up to three times, and has a characteristic S-shape that appears everywhere from physics equations to economic models.

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.

Cubic Graph Essentials Positive vs Negative Cubic Shapes Key Features of Cubic Graphs

Practice Questions for Cubic Graphs

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

Quick Recall 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)

11 questions on Cubic Graphs — practise free

Instant marking, adaptive difficulty, and 10 spaced repetition flashcards. Free until your GCSEs.

Try PrepWise Free

Back to

Cubic Graphs

Cubic Graph Essentials