Manipulation Of Quadratic Expressions
Overview
Quadratic expressions appear everywhere in mathematics, from modelling projectile trajectories to optimising areas and profits. Mastering the art of reshaping them through factorisation and completing the square gives you direct access to a quadratic's roots, vertex and symmetry, all without reaching for the formula.
In this topic you will learn two powerful rewriting techniques: factorising a quadratic into a product of linear factors and completing the square to reveal the turning point. Both are essential tools for the rest of the 4PM1 course and appear frequently in Edexcel exam questions.
Objectives
- Factorise quadratic expressions
- Complete the square for quadratic expressions
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 Manipulation Of Quadratic Expressions. 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 is the factorised form of x^2 + 7x + 10? A) (x + 2)(x + 5) B) (x + 1)(x + 10) C) (x - 2)(x - 5) D) (x + 3)(x + 4) Answer: A
- Which expression is equivalent to (x + 4)^2 - 9? A) x^2 + 8x + 7 B) x^2 + 8x + 25 C) x^2 + 4x + 7 D) x^2 + 16x + 7 Answer: A
- What is the vertex of the parabola y = (x - 3)^2 + 2? A) (3, 2) B) (-3, 2) C) (3, -2) D) (-3, -2) Answer: A
- Factorise 9x^2 - 16. A) (3x + 4)(3x - 4) B) (9x + 4)(x - 4) C) (3x + 8)(3x - 2) D) (3x - 4)^2 Answer: A
- When completing the square for x^2 - 12x + 5, what value is subtracted inside the bracket? A) 36 B) 12 C) 6 D) 144 Answer: A
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Practice Mock Questions
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