Solving Quadratic Equations: From Factoring to the Quadratic Formula
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Students will solve quadratic equations using multiple algebraic methods (factoring, completing the square, quadratic formula) and interpret the discriminant to determine the nature of solutions, connecting procedures to real-world contexts.
Lesson Overview
Students progress from identifying quadratic structure through factoring, completing the square, and applying the quadratic formula, culminating in discriminant analysis and real-world modeling. Each task changes exactly one variable in complexity.
Materials
- Vertical whiteboards or large chart paper
- Dry-erase markers (multiple colors)
- Pencils and scratch paper
- Basic calculator (phone calculator is fine)
Scaffolded Task Progression
Hint: Find two numbers that multiply to and add to .
[ Interactive graph / diagram, available in the full lesson ]
A drone's horizontal distance (in meters) from its launch pad follows at two checkpoints. Find those distances.
[ Interactive graph / diagram, available in the full lesson ]
A ball is thrown and its height (ft) satisfies at two moments. Find those values.
[ Interactive graph / diagram, available in the full lesson ]
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