Lesson Plan

• Describe the standard form of a quadratic equation and identify its coefficients.
• Apply factorisation, completing the square, and the quadratic formula to solve quadratic equations.
• Analyse the discriminant to determine the nature of the roots of a quadratic.
• Solve quadratic inequalities using sign charts and interpret the solution sets.
• Evaluate common pitfalls and select the most efficient method in exam contexts.

• Projector and screen
• Whiteboard and markers
• Graph paper and calculators
• Worksheet with mixed quadratic equations and inequalities
• Printed discriminant reference table
• Quadratic‑formula cue cards

Begin with a quick visual of a parabola from a real‑world context (e.g., a basketball shot) to capture interest. Review the standard form $ax^{2}+bx+c=0$ and ask students to identify $a$, $b$, $c$ in a displayed example. State that by the end of the lesson they will be able to solve any quadratic, classify its roots, and handle related inequalities.

1. Do‑now (5′): Write the standard form for three given quadratics and label $a$, $b$, $c$.
2. Mini‑lecture (10′): Derive the quadratic formula via completing the square; introduce the discriminant and its meaning.
3. Guided practice (12′): Solve one equation by factorisation, one by completing the square, and one using the formula; discuss efficiency.
4. Independent practice (15′): Worksheet – students solve a set of equations, state the discriminant, and classify the roots.
5. Quadratic inequalities (10′): Demonstrate the sign‑chart method; students complete a sample inequality on their own.
6. Exit ticket (3′): Write one tip for choosing the quickest solving method and give the solution set for a provided inequality.

Recap the three solving techniques, the role of the discriminant, and how sign charts resolve inequalities. Collect exit tickets to gauge understanding and assign homework: complete the additional worksheet that mixes factorisable, non‑factorisable, and inequality problems.