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.
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.
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
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)