Year 10 - Maths
Key features of a cubic graph
Non-linear graphs
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit graphical representations of non-linear graphs are introduced and explored, and their key features identified.
Lesson Summary
You will learn to identify the key features of a cubic graph.
Key Notes
- A cubic graph has a distinct shape.
- The roots of a cubic graph are where the graph intersects with the x-axis.
- The turning points are the local maximum and local minimum points of the graph.
Vocabulary To Learn
- Cubic: A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3
- Roots: When drawing the graph of an equation, the roots of the equation are where its graph intercepts the x-axis (where y = 0).
- Turning point: The turning point of a graph is a point on the curve where, as x increases, the y values change from decreasing to increasing or vice versa.
Common Mistakes To Avoid
- $$y=x^3$$ has one root so all cubic graphs have one root.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A cubic graph has a distinct shape. The roots of a cubic graph are where the graph intersects with the x-axis.
2. Use this key word in a maths sentence and explain it clearly. 'Cubic'
A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: $$y=x^3$$ has one root so all cubic graphs have one root. Correction: Make sure pupils see a wide variety of cubic graphs; ones with one root, two roots and three roots and link every one back to its equation and that the highest exponent of the variable is $$3$$ so they are all cubic graphs.
More Lessons In This Unit
- Advanced problem solving with non-linear graphs Study Guide
- Checking and securing understanding of drawing quadratic graphs Study Guide
- Drawing cubic graphs Study Guide
- Drawing exponential graphs Study Guide
- Drawing reciprocal graphs Study Guide
- Drawing the graph for the equation of a circle Study Guide
- Key features of a quadratic graph Study Guide
- Key features of a reciprocal graph Study Guide
- Key features of an exponential graph Study Guide
- Problem solving with non-linear graphs Study Guide
Browse all guides in the Year 10 Maths guide library.