Unit 8

Quadratic Functions

Explore quadratic functions and parabolas. Graph using vertex form and standard form, solve quadratic equations by factoring, square roots, completing the square, and the quadratic formula, apply the discriminant, work with complex solutions, and model real-world situations.

Unit 8 · 12 pages

Chapters

00Cover

Cover

Unit overview, essential questions, learning objectives, and vocabulary list for Unit 8 Quadratic Functions.

8.1

Introduction to Quadratic Functions

Identify quadratic functions, understand the shape of a parabola, and explore key features including vertex, axis of symmetry, and direction of opening.

8.2

Graphing Quadratic Functions

Graph quadratic functions in standard form by finding the vertex, axis of symmetry, and additional points.

8.3

Vertex Form

Write and interpret quadratic functions in vertex form y = a(x - h)^2 + k. Identify transformations and convert between standard and vertex form.

8.4

Solving Quadratics by Factoring

Solve quadratic equations by factoring, applying the zero product property to find roots and x-intercepts.

8.5

The Quadratic Formula

Solve any quadratic equation using the quadratic formula. Use the discriminant to determine the number and type of solutions.

8.6

The Discriminant and Nature of Roots

Use the discriminant b²−4ac to determine the number and type of solutions of a quadratic equation.

8.7

Completing the Square

Solve quadratic equations and convert to vertex form by completing the square.

8.8

Complex and Imaginary Numbers

Simplify expressions with imaginary unit i and find complex solutions of quadratic equations.

8.9

Solving Quadratic Equations by Square Roots

Apply the square root property to solve quadratic equations efficiently when no bx term is present.

8.10

Quadratic Applications and Modeling

Apply quadratic functions to projectile motion, area, revenue, and optimization problems.

8.11

Unit Review

Review all Unit 8 Quadratic Functions topics — graphing, vertex form, factoring, square roots, applications, and the quadratic formula — before the unit assessment.

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