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A cubic graph has an S-shaped form: y = x³ passes through the origin and rises from bottom left to top right. Free IGCSE Maths notes and 9 FAQs.
Cubic Graphs is part of Quadratic and Other Graphs in IGCSE Edexcel Higher Maths.
2 min
Reading time
20
Lessons in this topic
IGCSE Edexcel Higher
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Content review
A cubic graph has an S-shaped form: y = x³ passes through the origin and rises from bottom left to top right. Free IGCSE Maths notes and 9 FAQs.
Use this lesson to stay inside Quadratic and Other Graphs while connecting the detail back to the wider Topic 3: Sequences, Functions and Graphs topic.
Read the core explanations from Cubic Graphs before testing yourself from memory.
A cubic graph is different from a straight line and different from a quadratic. Its basic shape curves in one direction, flattens, then curves the other way.
At this level, the goal is not advanced analysis. It is secure visual recognition, sensible sketching and linking equations to shape.
Worked example: Sketching y = x cubed
Describe the graph of y = x^3 and give a few key points.
Answer: A rising cubic passing through (-2,-8), (-1,-1), (0,0), (1,1), (2,8).
Worked example: Interpreting a shifted cubic
Describe the effect of y = x^3 + 2 compared with y = x^3.
Answer: It is the graph of y = x^3 shifted 2 units upward.
Worked example: Recognising a More General Cubic
Explain why y = 2x^3 - 2x^2 + x - 1 is still a cubic graph.
Answer: It is cubic because the highest power is x^3.
A cubic sketch should be smooth and continuous. Do not draw sharp corners or make it look like two separate curves.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
A cubic graph has an S-shaped form: y = x³ passes through the origin and rises from bottom left to top right, curving one way, flattening, then curving the other way. If the coefficient is negative, it falls from top left to bottom right instead.
Choose simple x-values such as -2, -1, 0, 1 and 2, giving y-values -8, -1, 0, 1 and 8. Plot (-2,-8), (-1,-1), (0,0), (1,1) and (2,8) and join them with a smooth S-shape through the origin, with no sharp corners.
An equation is cubic if the highest power of x is 3, of the form Ax³ + Bx² + Cx + D. For example, y = 2x³ - 2x² + x - 1 is cubic; the extra terms change its shape and position but not its family.
The graph of y = x³ + 2 is the graph of y = x³ shifted 2 units upward, because each y-value is 2 more. The y-intercept moves from 0 to 2, and the shape stays cubic.
The graph of y = x³ has symmetry about the origin, which means it matches itself after a half-turn about the origin. For example, (2, 8) and (-2, -8) are both on the curve.
If the coefficient of x³ is negative, the cubic falls from top left to bottom right instead of rising from bottom left to top right. Ignoring the effect of a negative sign on the overall direction is a common pitfall.
A cubic graph has an S-shaped form that curves in one direction, flattens, then curves the other way, and its highest power of x is 3. A quadratic is also curved, so confusing the two is a common pitfall.
For y = x³, x = -2, -1, 0, 1, 2 give y = -8, -1, 0, 1, 8. The graph passes through the origin and rises through (-2,-8), (-1,-1), (0,0), (1,1) and (2,8).
A cubic graph does not have a sharp corner at the origin; it flattens smoothly. A cubic sketch should be smooth and continuous, not drawn with corners or as two separate curves.