Year 10 - Maths
Solving quadratic equations by completing the square
Algebraic manipulation
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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 algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.
Lesson Summary
You will learn to solve quadratic equations algebraically by completing the square.
Key Notes
- There are other methods to find the solutions of a quadratic equation.
- One of these methods is called completing the square.
- By representing this with a model, you can see why it has this name.
- Completing the square is useful when the quadratic cannot be easily factorised.
- The square root of a number can be positive or negative.
Vocabulary To Learn
- Completing the square: Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q
Common Mistakes To Avoid
- That we subtract the constant squared when the constant in the bracket is positive and add the constant squared when the constant in the bracket is negative.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are other methods to find the solutions of a quadratic equation. One of these methods is called completing the square.
2. Use this key word in a maths sentence and explain it clearly. 'Completing the square'
Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: That we subtract the constant squared when the constant in the bracket is positive and add the constant squared when the constant in the bracket is negative. Correction: Squaring a negative value gives a positive value. Whether the constant in the bracket is positive or negative, the square of the constant must always be subtracted. This can be made clearer with algebra tiles or area models.
More Lessons In This Unit
- Advanced problem solving with algebraic manipulation Study Guide
- Checking and securing understanding of changing the subject Study Guide
- Checking and securing understanding of expanding a single bracket Study Guide
- Checking and securing understanding of factorising Study Guide
- Checking and securing understanding of forming linear equations Study Guide
- Checking and securing understanding of simplifying Study Guide
- Checking and securing understanding of solving and interpreting linear equations Study Guide
- Checking and securing understanding of substitution Study Guide
- Checking and securing understanding of the product of two binomials Study Guide
- Factorising a quadratic expression Study Guide
- Factorising quadratics of the form ax^2 + bx + c Study Guide
- Factorising using the difference of two squares Study Guide
- Further algebraic terminology Study Guide
- Problem solving with algebraic manipulation Study Guide
- Solving complex quadratic equations by completing the square Study Guide
- Solving quadratic equations by factorising Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
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