Lesson Plan

• Describe the three possible natures of quadratic roots using the discriminant.
• Apply factorisation to solve quadratics that factor over the integers or simple rationals.
• Use the quadratic formula to find real roots of any quadratic.
• Complete the square to solve quadratics and to derive the vertex form.
• Select the most efficient method for a given quadratic equation.

• Whiteboard and markers
• Projector with slide deck
• Worksheet with practice problems
• Calculator (optional)
• Graph paper for sketching parabolas

Begin with a quick recall of the shape of a parabola and where it meets the x‑axis. Ask students to state how the discriminant indicates the number of real intercepts. Explain that today they will master three systematic methods to find those intercepts and will be able to select the quickest method for any quadratic.

1. Do‑now (5'): Solve a simple factorable quadratic on the board to activate prior knowledge.
2. Mini‑lecture (10'): Review standard form, discriminant, and introduce the three solving methods with brief examples.
3. Guided practice – Factorisation (10'): Work through the example 2x²‑5x‑3 together, checking each step.
4. Guided practice – Quadratic Formula (10'): Solve 3x²+2x‑8, emphasising calculation of D and interpretation.
5. Guided practice – Completing the Square (10'): Demonstrate with x²+6x+5, highlighting the transformation to (x‑h)².
6. Independent practice (15'): Students attempt the four practice questions while the teacher circulates.
7. Quick check (5'): Exit ticket – write which method they would use for a given quadratic and why.

Summarise the key steps of each method and remind students how the discriminant guides their choice. Collect the exit tickets to gauge understanding, and assign a homework sheet with mixed‑method problems for further practice.