Lesson Plan

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Lesson Plan
Grade: 10 Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Find the maximum or minimum value of a quadratic function by completing the square or by differentiation
Learning Objective/s:
  • Describe how the vertex form of a quadratic reveals its maximum or minimum value.
  • Apply completing the square to rewrite a quadratic in vertex form and identify the extremum.
  • Use differentiation to locate the stationary point of a quadratic and determine its nature.
  • Compare the two methods and explain why they produce the same vertex coordinates.
Materials Needed:
  • Projector and screen
  • Whiteboard and markers
  • Student worksheets with examples and practice questions
  • Graphing calculators (or calculator apps)
  • Printed summary handout of the two methods
  • PowerPoint slides illustrating the steps
 Introduction:
Begin with a real‑world optimisation scenario (e.g., finding the highest point of a thrown ball) to hook interest. Review that students already know the standard form of a quadratic and basic differentiation. State that by the end of the lesson they will be able to determine the maximum or minimum of any quadratic using either completing the square or differentiation and justify their answer.
Lesson Structure:
  1. Do‑now (5'): Quick mental rewrite of a given quadratic into vertex form on the board.
  2. Mini‑lecture (10'): Explain vertex form, demonstrate completing the square step‑by‑step.
  3. Guided practice (15'): Teacher models the method on the example \(f(x)=-3x^{2}+12x-5\); students follow in their worksheets.
  4. Differentiation method (10'): Derive \(f'(x)=2ax+b\), solve for \(x\), substitute back; work through \(g(x)=4x^{2}-8x+3\) together.
  5. Independent practice (15'): Students attempt the four practice questions, peer‑check answers, teacher circulates for support.
  6. Exit ticket (5'): Write one concise reason why both methods give the same vertex \((h,k)\).
Conclusion:
Recap that the vertex \((h,k)\) can be found either by completing the square or by setting the derivative to zero, and the sign of \(a\) tells us whether the extremum is a maximum or minimum. Collect exit tickets and remind students that their homework is to complete the additional worksheet, solving two new quadratics with both methods.