This topic summary covers Topic Summary: 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 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 10 of 10
Practice
11 questions
Recall
10 flashcards
Topic Summary: Cubic Graphs
Key Facts
- General form: y = ax³ + bx² + cx + d
- a > 0: rises bottom-left to top-right
- a < 0: falls top-left to bottom-right
- Always at least 1 real root
- Has 0 or 2 turning points (never 1)
Sketching Steps (Factorised Form)
- 1. Find roots: set each bracket to zero
- 2. Find y-intercept: substitute x = 0
- 3. Check sign of a (shape direction)
- 4. Sketch smooth curve through roots and y-intercept
Key Vocabulary
- Cubic: polynomial of degree 3
- Point of inflection: momentarily flat, no turning point
- Repeated root: curve touches axis without crossing
- Turning point: local max or min of the curve
Common Errors
- Drawing straight line segments instead of a smooth curve
- Making a cubic cross at a repeated root (should touch)
- Assuming all cubics have an S-shape (many have a hill-valley shape)
- Thinking cubics can only cross x-axis once