Year 10 - Maths
Key features of a quadratic 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 quadratic graph.
Key Notes
- A quadratic graph is a parabola.
- The roots of a quadratic graph are where the graph intersects with the x-axis.
- The turning point is the maximum or minimum point of the graph.
- The coordinates of the turning point can be found by completing the square.
Vocabulary To Learn
- 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
- Parabolas are 'upwards' or 'downwards'.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A quadratic graph is a parabola. The roots of a quadratic graph are where the graph intersects with the x-axis.
2. Use this key word in a maths sentence and explain it clearly. 'Roots'
When drawing the graph of an equation, the roots of the equation are where its graph intercepts the x-axis (where y = 0). Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Parabolas are 'upwards' or 'downwards'. Correction: Encourage use of language such as "The turning point of this parabola is a maximum/minimum value" and "As the absolute values of $$x$$ increase, the $$y$$ values decrease/increase".
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 cubic 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.