About Course

This course is a complete and focused exploration of quadratic equations, a cornerstone of Algebra I and II. Students will learn how to solve quadratics using factoring, completing the square, the quadratic formula, and graphing. They will interpret parabolic graphs, use the discriminant to predict solution types, and apply quadratic models to real-world word problems. With clear instruction, structured lessons, and scaffolded practice, students will gain confidence, fluency, and a deeper understanding of one of algebra’s most essential topics.

Ideal for learners preparing for standardized exams, reinforcing classroom instruction, or building a stronger algebra foundation, this course brings clarity, application, and strategy together in one powerful learning experience.

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Course Content

1. Understanding Quadratic Equations
This topic introduces students to what makes an equation quadratic, how to identify key components, and how different algebraic forms affect both solving and graphing. By recognizing the structure and purpose of standard, vertex, and factored forms, students begin developing flexibility and awareness in manipulating and interpreting quadratic functions.

  • 1.1 What is a Quadratic Equation?
  • 1.2 Lesson: Identifying Coefficients and Understanding the Role of a, b, and c
  • 1.3 Converting Between Standard, Vertex, and Factored Forms

2. Solving Quadratics by Factoring
Factoring is a fundamental method for solving quadratics efficiently when possible. This topic covers factoring trinomials when the leading coefficient is 1 or not 1, as well as identifying and solving using special patterns such as perfect square trinomials and the difference of squares. Students learn how factoring reveals x-intercepts and connects to graphing.

3. Solving by Completing the Square
Completing the square is a critical method that transforms standard form into vertex form, while also providing a powerful strategy for solving equations algebraically. Students will learn the structured process for completing the square and how it connects to graphing parabolas and understanding function behavior.

4. Solving with the Quadratic Formula
The quadratic formula is a universal solving method that works for all quadratic equations. Students will learn how to derive, memorize, and apply the formula, practice substitution and simplification techniques, and understand common errors to avoid. This topic reinforces precision and fluency in symbolic manipulation.

5. Discriminant Analysis
The discriminant (the expression under the square root in the quadratic formula) is a predictive tool that reveals the number and type of solutions before solving. Students will learn to analyze the discriminant, interpret whether solutions are real or complex, and make connections between algebraic results and graphical features of the parabola.

6. Graphing Quadratic Equations
Students will gain visual and conceptual fluency in graphing quadratic functions. This topic covers all forms of quadratics and how to extract key information: vertex, intercepts, axis of symmetry, direction of opening, and transformations. Students will also use tables, calculators, and digital tools to support their graphing skills.

7. Word Problems with Quadratics
This topic brings together all prior learning and applies it to real-world contexts. Students will analyze and model scenarios involving area, revenue, projectile motion, and optimization. They will learn how to create equations from word problems, determine the appropriate solving method, and interpret their results meaningfully.

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