Unit 6: Quadratic Functions & Equations
In this unit, you will learn how to graph quadratic functions, solve quadratic equations using various methods, understand complex roots, and apply transformations. By the end of this unit, you will be able to analyze and manipulate quadratic functions in a variety of contexts.
Unit Goals
- Graph quadratic functions and identify vertex, axis of symmetry, intercepts, and direction of opening.
- Solve quadratic equations by square roots, completing the square, and the quadratic formula.
- Use the discriminant to determine the nature of roots (real vs complex).
- Apply quadratics to real-world problems (projectiles, area models).
- Work with complex numbers when quadratic roots are nonreal and perform basic operations.
- Analyze transformations of quadratic graphs (shifts, stretches, reflections).
Lessons
- Lesson 33 — Graphing Quadratic Functions (Parabolas, Vertex, Axis of Symmetry)
- Lesson 34 — Solving Quadratics by Square Roots
- Lesson 35 — Completing the Square
- Lesson 36 — Quadratic Formula and the Discriminant
- Lesson 37 — Applications of Quadratics (Projectiles, Area Problems)
- Lesson 38 — Complex Numbers (Introduction, Operations)
- Lesson 39 — Solving Quadratic Equations with Complex Roots
- Lesson 40 — Transformations of Quadratic Functions