Unit 8 — Quadratic Functions

Unit 8 · Quadratic Functions

Quadratic Functions

Explore parabolas, graph quadratics in standard and vertex form, solve quadratic equations by factoring, square roots, completing the square, and the quadratic formula, and apply them to real-world problems.

Estimated Time

30–40 minutes

Difficulty

Intermediate

11 Lessons
8 Learning Goals
12 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 8 — Quadratic Functions takes you beyond straight lines. You will explore parabolas, graph quadratics in standard and vertex form, solve quadratic equations by factoring and the quadratic formula, and apply them to real-world problems like projectile motion.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Identify quadratic functions and describe the key features of a parabola.
Goal 2Graph quadratic functions in standard form by finding the vertex, axis of symmetry, and intercepts.
Goal 3Write and interpret quadratic functions in vertex form y = a(x − h)² + k.
Goal 4Solve quadratic equations by factoring using the zero product property.
Goal 5Solve any quadratic equation using the quadratic formula.
Goal 6Use the discriminant to determine the number and type of solutions.
Goal 7Solve quadratic equations using the square root property.
Goal 8Apply quadratic functions to real-world problems involving projectile motion, area, revenue, and optimization.

Skills You Will Master

Graphing parabolas
Vertex & standard form
Solving by factoring
Quadratic formula
Using the discriminant
Real-world applications

Real-World Connection

Quadratic functions describe the path of anything that flies through the air — a basketball, a rocket, a water fountain arc. Engineers use them to design suspension bridges and satellite dishes. Businesses use them to find the price that maximizes profit. Physicists use them to model the motion of falling objects under gravity. The quadratic formula is one of the most famous results in all of mathematics, and understanding it deeply gives you a powerful tool for solving problems that cannot be handled with linear equations alone.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter