Year 10 - Maths
Checking and securing understanding of drawing quadratic graphs
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 generate coordinate pairs for a quadratic graph from its equation and then draw the graph.
Key Notes
- A table of values can be useful to identify coordinate pairs which satisfy the equation.
- By substituting the values for x, you can calculate corresponding values for y.
- If used correctly, your calculator can be a powerful tool to speed up calculations.
Vocabulary To Learn
- Quadratic: A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2 The general form for a quadratic is $$ax^2 + bx + c$$
- Parabola: A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus), and a fixed straight line (the directrix).
Common Mistakes To Avoid
- To draw a graph, points should always be joined with line segments.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A table of values can be useful to identify coordinate pairs which satisfy the equation. By substituting the values for x, you can calculate corresponding values for y.
2. Use this key word in a maths sentence and explain it clearly. 'Quadratic'
A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2 The general form for a quadratic is $$ax^2 + bx + c$$. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: To draw a graph, points should always be joined with line segments. Correction: For the graph of $$y=x^2$$ show the line joining $$(0,0)$$ and $$(1,1)$$ and ask pupils to test some coordinate pairs from that line in the original equation. For example, $$(1/2,1/2)$$ does not satisfy the equation.
More Lessons In This Unit
- Advanced problem solving with non-linear 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 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
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