Sketching Curves
Overview
Every type of equation has a signature shape when you draw it: a straight line, a smooth U-shaped parabola, a wave, a curve that races away. Recognising these shapes lets you picture an equation at a glance and sketch it quickly without plotting dozens of points.
In this lesson you will recognise, sketch and interpret the graphs of linear and quadratic functions, and (at Extended) cubic, reciprocal and exponential functions, picking out their key features such as intercepts and turning points.
Objectives
- Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic.
- Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic (c) cubic (d) reciprocal (e) exponential. (Extended only)
Audio Lesson
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Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Sketching Curves. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What shape is the graph of y = x^2 - 4? A. A straight line B. A parabola C. An S-shape D. A circle Answer: B
- Where does y = x^2 - 4 cross the x-axis? A. x = -4 and x = 4 B. x = -2 and x = 2 C. x = 0 only D. x = 4 only Answer: B
- What is the vertex of y = x^2 - 4? A. (0, 0) B. (0, 4) C. (0, -4) D. (-4, 0) Answer: C
- The graph of y = mx + c is always: A. a parabola B. a straight line C. an S-shape D. a curve Answer: B
- If a is negative in y = ax^2 + bx + c, the parabola: A. opens upwards B. opens downwards C. is a straight line D. has no vertex Answer: B
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