Lesson Plan

• Describe how the discriminant Δ determines the nature of the roots of a quadratic equation.
• Explain the link between the sign of Δ and the geometric relationship between a line and a parabola.
• Apply the discriminant method to decide whether a line cuts, touches, or misses a given quadratic curve.
• Solve worked examples and practice questions using the Δ‑test.

• Projector or interactive whiteboard
• Prepared PowerPoint/Google Slides with diagrams
• Worksheet with practice questions
• Graph paper and coloured pencils
• Scientific calculators

Begin with a quick “guess the number of intersection points” visual using a parabola and a line. Review the previous lesson on solving quadratic equations and remind students of the formula for the discriminant. State that today they will learn to predict intersection behaviour without solving the equations.

1. Do‑now (5'): Students complete a short exit‑ticket from the previous lesson on finding roots.
2. Mini‑lecture (10'): Introduce the discriminant Δ = b²‑4ac and its three cases, linking each to the graph of y = ax²+bx+c.
3. Demonstration (8'): Show how substituting y = mx + c into the quadratic yields Δ' and interpret Δ' > 0, = 0, < 0 with dynamic graphing software.
4. Guided practice (12'): Work through the provided example (y = 3x‑4 and y = x²+2x+1) together, prompting students to calculate Δ' and state the result.
5. Independent practice (7'): Students tackle the three practice questions on worksheets, circulating to check reasoning.
6. Recap & exit ticket (3'): Quick verbal summary of key points; students write one condition for each of the three intersection types on a sticky note.

Re‑emphasise that the sign of the discriminant instantly tells us the nature of roots and the line‑parabola relationship. Collect exit tickets as a formative check and assign homework: complete a set of five new line‑parabola problems, recording Δ' and the geometric outcome.