Year 9 - Maths
Exploring the shapes of graphs using technology
Graphical representations
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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 pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.
Lesson Summary
You will learn to appreciate that different types of equations give rise to different graph shapes, identifying quadratics in particular.
Key Notes
- There are many different types of equations.
- You can plot the graph of an equation if you have two variables (one for each axis).
- Certain types of equation give rise to certain graph shapes.
- Linear equations produce a straight line.
- Quadratic equations produce a parabola.
Vocabulary To Learn
- Quadratic: A quadratic is an equation whereby the highest exponent of the variable is 2; the graph of which forms a parabola.
- 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 (a directrix).
Common Mistakes To Avoid
- After plotting the integer coordinate pairs of a quadratic, they should be joined with a straight line.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are many different types of equations. You can plot the graph of an equation if you have two variables (one for each axis).
2. Use this key word in a maths sentence and explain it clearly. 'Quadratic'
A quadratic is an equation whereby the highest exponent of the variable is 2; the graph of which forms a parabola. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: After plotting the integer coordinate pairs of a quadratic, they should be joined with a straight line. Correction: Use graphing technology to plot coordinate pairs that use smaller and smaller non-integer steps between $$x$$-coordinates. This will reveal the true, curved nature of the line.
More Lessons In This Unit
- Checking and securing understanding of non-linear sequences Study Guide
- Efficiently drawing linear graphs Study Guide
- Equations and their graphs Study Guide
- Extending thinking about sequences Study Guide
- Graphically solving two linear graphs that intersect Study Guide
- Modelling with graphs Study Guide
- Problem solving with graphical representations Study Guide
- Reading from graphs Study Guide
Browse all guides in the Year 9 Maths guide library.