x	x³	−3x	y
−2	−8	6	−2
−1	−1	3	2
0	0	0	0
1	1	−3	−2
2	8	−6	2
3	27	−9	18

This cubic has roots at x = −√3, 0, and √3. Local maximum at approximately x = −1 (y = 2) and local minimum at x = 1 (y = −2).

This deep dive covers Worked Example: Table of Values for y = x³ − 3x 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 6 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

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

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)

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.

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

Practice questions for Cubic Graphs

Quick recall flashcards

11 questions on Cubic Graphs: practise free