Year 10 - Maths
Solving quadratic equations by using the formula
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 using the formula.
Key Notes
- The quadratic formula can be derived from the general form of a quadratic equation.
- It can be derived by completing the square.
- The formula is useful when the quadratic cannot be easily factorised.
- Technology can be used to identify solutions and is useful for checking.
Vocabulary To Learn
- Quadratic formula: The quadratic formula is a formula for finding the solutions to any quadratic equation of the form ax^2 + bx + c = 0
Common Mistakes To Avoid
- Mistakes often occur when substituting into the quadratic formula with calculators, as pupils miss out brackets and change the priority of operations.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The quadratic formula can be derived from the general form of a quadratic equation. It can be derived by completing the square.
2. Use this key word in a maths sentence and explain it clearly. 'Quadratic formula'
The quadratic formula is a formula for finding the solutions to any quadratic equation of the form ax^2 + bx + c = 0. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Mistakes often occur when substituting into the quadratic formula with calculators, as pupils miss out brackets and change the priority of operations. Correction: Values should always be put in brackets when substituted. This avoids mistakes when squaring and subtracting negative values. It also makes it easier to change the values of a , b , and c when working on a new question.
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 completing the square Study Guide
- Solving quadratic equations by factorising Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- The product of three binomials Study Guide
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