Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Solve quadratic equations using various methods.
• Determine the nature of roots using the discriminant.
• Graph quadratic functions and interpret their features.
• Solve quadratic inequalities.
• Apply quadratic functions to real-life situations.

Lesson summary

This lesson transitions from solving quadratic *equations*, which give us specific points (like when a ball hits the ground), to solving quadratic *inequalities*. Inequalities help us find a *range* of possibilities. For example, a small business owner in Kejetia Market doesn't just want to know the exact number of items to sell to break even; they want to know the *range* of sales that will guarantee a profit. Quadratic inequalities provide the mathematical tools to answer such questions, making them essential for modelling real-world scenarios in business, science, and engineering. We will build on our knowledge of factorisation and graphing to master this important skill.

Lesson notes

Part 1: From Quadratic Equations to Inequalities (Recall and Bridge)

Let's start with what we already know. A quadratic equation is of the form `ax² + bx + c = 0`. When we solve it, we find the specific values of `x` where the function's value is exactly zero. Graphically, these are the x-intercepts or roots of the parabola.

Example Recall: Solve the equation `x² - x - 6 = 0`. Method: Factorisation. We need two numbers that multiply to -6 and add to -1. These are -3 and +2. `(x - 3)(x + 2) = 0` Solution: `x = 3` or `x = -2`.

Now, consider a quadratic inequality. It uses symbols like ` `, `≤`, or `≥`. `x² - x - 6 > 0` `x² - x - 6 ≤ 0`

Evaluation guide

• Describe the processes of solving quadratic equations by graphical method, factorisation,
• and inspection for quadratic functions, including functions of the form ( 𝑥𝑥)=49) where
• possible.
• Collaborative Learning : Learners to work in convenient groups (ability, mixed -ability, mixed gender,