Course Description
Quadratics are one of the most important topics in mathematics and appear throughout Algebra, Geometry, SAT, PSAT, ACT, AP courses, and higher mathematics. This complete course is designed to take students from absolute beginner level to advanced problem-solving mastery in quadratics.
The course starts with the fundamentals of algebra and gradually builds toward advanced applications, graph analysis, transformations, modeling, SAT-style objective questions, and real-world applications. Every concept is explained step-by-step with visual understanding, examples, worksheets, quizzes, and exam-style practice questions.
Students will learn how to confidently solve quadratic equations using multiple methods, analyze graphs of quadratic functions, understand vertex form and transformations, factor complex expressions, and apply quadratics in geometry, physics, and word problems.
Whether you are struggling with basics or aiming for top scores in school exams and standardized tests, this course provides a complete roadmap to mastery.
Who This Course Is For
- Students in Grades 8–10
- SAT / PSAT / ACT preparation students
- Homeschool students
- Students preparing for Algebra 1 and Algebra 2
- Students who want stronger foundations in mathematics
- Parents looking for a complete quadratic learning program
What Students Will Learn
By the end of this course, students will be able to:
- Understand quadratic expressions and equations
- Factor quadratics confidently
- Solve quadratic equations using multiple methods
- Graph quadratic functions accurately
- Understand vertex form and transformations
- Use the quadratic formula effectively
- Analyze discriminants and roots
- Solve SAT-style and school-level problems
- Apply quadratics to real-world situations
- Build strong algebraic thinking and problem-solving skills
Table of Contents
MODULE 1 — Algebra Foundations
- Variables and Expressions
- Order of Operations
- Simplifying Algebraic Expressions
- Combining Like Terms
- Exponents and Powers
- Laws of Exponents
- Linear Equations Review
- Coordinate Plane Basics
- Introduction to Functions
MODULE 2 — Introduction to Quadratics
- What is a Quadratic?
- Identifying Quadratic Expressions
- Standard Form of a Quadratic
- Degree of a Polynomial
- Understanding Parabolas
- Real-Life Examples of Quadratics
MODULE 3 — Multiplying Polynomials
- Monomials and Polynomials
- Multiplying Binomials
- FOIL Method
- Special Products
- Difference of Squares
- Perfect Square Trinomials
- Expanding Quadratic Expressions
MODULE 4 — Factoring Basics
- Greatest Common Factor (GCF)
- Factoring by Grouping
- Factoring Simple Trinomials
- Factoring Trinomials with Leading Coefficient 1
- Factoring Trinomials with Leading Coefficient Greater Than 1
- Factoring Difference of Squares
- Factoring Perfect Square Trinomials
- Mixed Factoring Practice
MODULE 5 — Solving Quadratic Equations
- Solving by Factoring
- Zero Product Property
- Solving Simple Quadratics
- Solving Quadratics with Leading Coefficient Greater Than 1
- Solving Quadratics with Multiple Factoring Methods
- Checking Solutions
MODULE 6 — Graphing Quadratic Functions
- Introduction to Quadratic Graphs
- Shape and Direction of Parabolas
- Axis of Symmetry
- Vertex of a Parabola
- Finding Intercepts
- Graphing from Standard Form
- Maximum and Minimum Values
- Domain and Range
MODULE 7 — Vertex Form and Transformations
- Vertex Form of Quadratics
- Converting Standard Form to Vertex Form
- Completing the Square
- Horizontal and Vertical Shifts
- Stretching and Compressing Graphs
- Reflection Across Axes
- Transformations Practice
MODULE 8 — Solving by Completing the Square
- Why Completing the Square Works
- Completing the Square with Leading Coefficient 1
- Completing the Square with Leading Coefficient Greater Than 1
- Solving Equations Using Completing the Square
- Applications of Completing the Square
MODULE 9 — Quadratic Formula
- Deriving the Quadratic Formula
- Using the Quadratic Formula
- Simplifying Radicals in Answers
- Understanding Two Solutions
- Choosing Best Solving Method
- SAT-Style Quadratic Formula Questions
MODULE 10 — Discriminant and Nature of Roots
- What is the Discriminant?
- Predicting Number of Solutions
- Real vs Imaginary Roots
- Repeated Roots
- Graphical Meaning of the Discriminant
MODULE 11 — Applications of Quadratics
- Projectile Motion Problems
- Area and Geometry Problems
- Revenue and Profit Models
- Optimization Problems
- Word Problems with Quadratics
- Real-World Modeling
MODULE 12 — Advanced Quadratic Concepts
- Quadratic Inequalities
- Solving Quadratic Inequalities Graphically
- Systems with Linear and Quadratic Equations
- Intersections of Graphs
- Complex and Imaginary Solutions
- Introduction to Polynomial Functions
- Higher-Level Problem Solving
MODULE 13 — SAT / ACT / Exam Preparation
- SAT-Style Multiple Choice Questions
- Grid-In Questions
- Common Mistakes and Traps
- Time-Saving Techniques
- Calculator vs Non-Calculator Strategies
- Mixed Difficulty Practice Sets
- Challenge Problems
MODULE 14 — Final Mastery Section
- Complete Quadratics Revision
- Formula Sheet Review
- Mixed Concept Tests
- Real Exam Simulations
- Advanced Challenge Test
- Final Course Project
- Certificate Assessment
Bonus Resources
- Printable Worksheets
- Chapter-wise Quizzes
- Video Solutions
- SAT Practice Sets
- Formula Cheat Sheets
- Homework Assignments
- Parent Progress Tracker
- Doubt Support Community
Curriculum
- 1 Section
- 0 Lessons
- 15 Weeks
- Algebra BasicsSolving Linear equations in 1 variable.1
Instructor
