Lesson Plan: Comparing Forms of Quadratic Functions

In this seventh lesson of the Quadratic Functions and Equations Unit, students will learn how to compare different forms of quadratic equations. Quadratic functions can be expressed in multiple forms, each providing unique insights into the function's behavior and key characteristics.

Students will:

• Identify and compare the standard form (y = ax² + bx + c), vertex form (y = a(x - h)² + k), and factored form (y = a(x - r₁)(x - r₂)) of quadratic equations
• Analyze how each form reveals different properties of a quadratic function, such as the vertex, axis of symmetry, and roots
• Convert quadratic equations between standard, vertex, and factored forms
• Explore how different forms are used to solve problems and interpret graphs
• Apply knowledge of quadratic forms to solve real-world scenarios

Designed for Algebra 1 and Algebra 2 students, this lesson aligns with Common Core standards and deepens students' understanding of quadratic functions. By comparing different forms, students will develop flexibility in solving quadratic equations and analyzing their graphical representations.

This is the seventh lesson in a ten-part unit on quadratic functions and equations. Future lessons will focus on advanced methods for solving and interpreting quadratics.

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