Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

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Performance objectives

• Define quadratic inequalities.
• Solve quadratic inequalities algebraically and graphically.
• Model real-life problems using quadratic inequalities.
• Use tools like graphs to visualize solutions.

Lesson summary

This lesson focuses on a powerful application of algebra: using quadratic inequalities to model and solve real-world problems. We often encounter situations where a quantity must be *greater than*, *less than*, or *at least* a certain value, not just equal to it. For example, a business owner wants their profit to be *more than* zero, a farmer needs a fenced area to be *at least* a certain size, or an engineer must ensure the stress on a beam is *below* a critical limit. By translating these scenarios into quadratic inequalities, we can determine a range of possible and safe solutions.

Lesson notes

Core Idea: A quadratic inequality is a mathematical statement that relates a quadratic expression to a value using an inequality symbol ( , ≤, ≥). The general form is `ax² + bx + c > 0` (or with any other inequality symbol). Solving it means finding all the values of the variable (e.g., `x`) that make the statement true.

Recap (5 minutes - Think-Pair-Share): How do we solve a quadratic *equation* like `x² - 5x + 6 = 0`? (Answer: Factoring, quadratic formula, completing the square to find roots `x=2` and `x=3`). How do we represent `x > 3` on a number line? (Answer: Open circle at 3, arrow pointing right).

Step-by-Step Method for Solving Quadratic Inequalities

Let's learn a reliable method for solving any one-variable quadratic inequality. We will use the example: Solve `x² - x - 6 > 0`.

Evaluation guide

• Solve quadratic inequalities involving real life problems.
• Collaborative Learning : Learners to work in convenient groups (ability, mixed -ability, mixed gender,
• etc.) to model real life problems involving quadratic inequalities and present answers.
• Talk for Learning Approaches: learners brainstorm through think -pair- share, building on what others