Quadratic Modeling and Optimization
Applying quadratic functions to solve real-world optimization problems (e.g., maximizing area, projectile motion).
Key Questions
- Analyze how the vertex of a parabola represents a maximum or minimum value in real-world contexts.
- Design a quadratic model to represent a given optimization problem.
- Evaluate the limitations of using a quadratic model for long-term predictions in certain scenarios.
Ontario Curriculum Expectations
Suggested Methodologies
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Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
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Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
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More in Quadratic Functions and Equations
Review of Quadratic Forms and Graphing
Reviewing standard, vertex, and factored forms of quadratic functions and their graphical properties (vertex, axis of symmetry, intercepts).
2 methodologies
Solving Quadratics by Factoring and Square Roots
Mastering solving quadratic equations using factoring and the square root property.
2 methodologies
Completing the Square
Using the method of completing the square to solve quadratic equations and convert standard form to vertex form.
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The Quadratic Formula and Discriminant
Applying the quadratic formula to solve equations and using the discriminant to determine the nature of roots.
2 methodologies
Complex Numbers
Introducing imaginary numbers, complex numbers, and performing basic operations (addition, subtraction, multiplication) with them.
2 methodologies