This deep dive covers Drawing a Cubic Graph 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 5 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 5 of 10
Practice
11 questions
Recall
10 flashcards
Drawing a Cubic Graph
From a Factorised Form
If given y = (x − a)(x − b)(x − c):
- Find roots: set each bracket to zero → x = a, x = b, x = c
- Find y-intercept: set x = 0, multiply all brackets
- Identify the shape: positive leading coefficient → positive cubic shape
- Plot the roots and y-intercept, sketch a smooth S-shaped curve through them
Example: Sketch y = (x + 1)(x − 2)(x − 3)
Roots: x = −1, x = 2, x = 3 (set each bracket to zero)
y-intercept: (0 + 1)(0 − 2)(0 − 3) = 1 × (−2) × (−3) = 6 → point (0, 6)
Leading term is x³ (positive), so positive cubic shape.
Sketch: rises from bottom-left, crosses at x = −1, dips below x-axis, crosses at x = 2, rises above, crosses at x = 3, continues upward.
From a Table of Values
- Choose a range of x-values (e.g. −3 to 3)
- Substitute each value into the equation to calculate y
- Plot all points carefully
- Join with a smooth S-shaped curve — no sharp corners or straight segments