Quadratic Functions & Equations in Algebra 1

Overview

• This unit explores quadratic functions and equations within the Algebra 1 course offered by Khan Academy.
• The focus is on understanding parabolas and applying quadratic functions to real-world problems.

Unit Structure

1. Intro to Parabolas

• Learn:
  • Introduction to Parabolas
  • Interpreting parabolas in context
  • Interpreting a quadratic graph
• Practice:
  • Exercises to reinforce understanding of parabolas

2. Solving and Graphing with Factored Form

• Learn:
  • Zero product property
  • Graphing quadratics in factored form
  • Quadratic word problems with factored form
• Practice:
  • Exercises on solving quadratic equations using factored form

3. Solving by Taking the Square Root

• Learn:
  • Solving quadratics by taking square roots
  • Strategies and steps involved
• Practice:
  • Exercises to practice solving quadratics by taking square roots

4. Vertex Form

• Learn:
  • Understanding vertex form
  • Graphing quadratics using vertex form
  • Solving quadratic word problems in vertex form
• Practice:
  • Exercises related to vertex form

5. Solving Quadratics by Factoring

• Learn:
  • Methods for factoring quadratics
  • Using structure to solve equations
  • Word problems involving quadratic equations
• Practice:
  • Factoring exercises to solve quadratics

6. The Quadratic Formula

• Learn:
  • Introduction to the quadratic formula
  • Understanding and applying the formula
  • Worked examples and review
• Practice:
  • Exercises on using the quadratic formula

7. Completing the Square

• Learn:
  • Introduction and intermediate lessons on completing the square
  • Solving equations by completing the square
  • Proof of the quadratic formula
• Practice:
  • Exercises to practice completing the square

8. Strategies for Solving Quadratics

• Learn:
  • Strategies and methods for solving quadratic equations

9. Quadratic Standard Form

• Learn:
  • Finding vertices in standard form
  • Graphing quadratics using standard form
  • Problem-solving applications
• Practice:
  • Exercises on standard form quadratics

10. Features & Forms of Quadratic Functions

• Learn:
  • Identifying features and forms of quadratic functions
  • Interpreting models in different forms
• Practice:
  • Exercises to identify and use quadratic forms

11. Comparing Quadratic Functions

• Learn:
  • Comparing features of quadratic functions
• Practice:
  • Exercises to compare quadratic functions

12. Transforming Quadratic Functions

• Learn:
  • Transformations including shifting, scaling, and reflecting parabolas
• Practice:
  • Exercises to practice transformations of parabolas

Quizzes and Unit Test

• Quizzes are available throughout the unit to test understanding and mastery of topics.
• A unit test is provided to assess overall proficiency in quadratic functions and equations.

Additional Resources

• Each topic includes links to video tutorials and practice exercises.
• The unit aims to build strong foundational skills in quadratic equations applicable to real-world problems.