Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Solve quadratic equations by factorization.
• Sketch graphs of y = ax² + q and y = a(x - p)².
• Determine the equation of a quadratic function from its graph.
• Apply quadratic equations to solve word problems.

Lesson summary

This week's focus is a comprehensive revision of the key concepts covered in Week 6, which will equip you with the necessary skills to tackle more complex problems and apply your mathematical knowledge to real-world scenarios. A solid understanding of these concepts is essential not only for your Grade 10 Mathematics marks but also for building a strong foundation for future mathematical studies and related fields. Think about how percentages are used in calculating discounts at your local Shoprite or how understanding patterns can help you plan your budget for the month. Mathematics is all around us!

Lesson notes

A. Solving Quadratic Equations by Factorization A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠

0. Solving a quadratic equation means finding the values of x that make the equation true (the roots or solutions). Factorization is a method used when the quadratic expression can be written as a product of two linear factors.

Why Factorization Works: The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero. This property is the foundation for solving quadratic equations by factorization. If we can write the quadratic equation as (x - r₁)(x - r₂) = 0, then either x - r₁ = 0 or x - r₂ = 0, which gives us the solutions x = r₁ and x = r₂.

How to Factorize: Ensure the equation is in the standard form: ax² + bx + c =

0. Factorize the quadratic expression: Find two numbers that multiply to give 'c' and add to give 'b'. Then write the expression as (x + number1)(x + number2) = 0 Apply the Zero Product Property: Set each factor equal to zero and solve for x.