Quadratic

UNIT 1

Foundations for Quadratics

Build the algebra skills needed to understand quadratic relationships.

1. What a Quadratic Is
2. Variables, Expressions and Equations
3. Order of Operations
4. Combining Like Terms
5. The Distributive Property
6. Solving Linear Equations Review
7. Why Quadratics Matter

UNIT 2

Powers and Square Roots

Understand squares, roots and the numerical structure behind quadratic equations.

1. Meaning of a Square
2. Perfect Squares
3. Square Roots
4. Estimating Square Roots
5. Exponent Rules
6. Radicals
7. Squares in Real Life

UNIT 3

Quadratic Expressions

Recognize, simplify and evaluate expressions containing squared variables.

1. Standard Quadratic Form
2. Leading Coefficient
3. Linear and Constant Terms
4. Evaluating Quadratic Expressions
5. Simplifying Quadratic Expressions
6. Classifying Quadratics
7. From Words to Expressions

UNIT 4

Multiplying Polynomials

Build quadratic expressions by multiplying linear factors.

1. Monomial Multiplication
2. Distributing Across Binomials
3. Binomial Times Binomial
4. The FOIL Pattern
5. Special Products
6. Squaring a Binomial
7. Multiplication in Context

UNIT 5

Factoring Foundations

Reverse multiplication to reveal the structure of quadratic expressions.

1. What Factoring Means
2. Greatest Common Factor
3. Factoring x² + bx + c
4. Finding Factor Pairs
5. Checking by Multiplication
6. Factoring with Negative Terms
7. Factoring Strategy

UNIT 6

Advanced Factoring

Factor quadratic expressions with coefficients and special patterns.

1. Factoring ax² + bx + c
2. The AC Method
3. Grouping
4. Difference of Squares
5. Perfect Square Trinomials
6. Choosing a Factoring Method
7. Factoring Completely

UNIT 7

Solving by Factoring

Use factors and the zero-product property to solve quadratic equations.

1. The Zero-Product Property
2. Setting an Equation Equal to Zero
3. Solving Simple Factored Equations
4. Solving Trinomials
5. Repeated Roots
6. Checking Solutions
7. Factoring Word Problems

UNIT 8

Graphing Parabolas

See quadratic equations as curves and understand their key features.

1. What a Parabola Is
2. Opening Up or Down
3. The Vertex
4. The Axis of Symmetry
5. Intercepts
6. Graphing from a Table
7. Reading a Quadratic Graph

UNIT 9

Vertex Form

Understand how y = a(x-h)²+k reveals the position and shape of a parabola.

1. Understanding Vertex Form
2. Horizontal Shifts
3. Vertical Shifts
4. Stretching and Compressing
5. Reflections
6. Writing Vertex Form from a Graph
7. Transforming Parabolas

UNIT 10

Completing the Square

Transform quadratic expressions into perfect squares and vertex form.

1. Why Complete the Square
2. Building a Perfect Square
3. Completing x² + bx
4. Solving by Completing the Square
5. When a Is Not One
6. Converting to Vertex Form
7. Geometric Meaning of Completing the Square

UNIT 11

The Quadratic Formula

Use a universal method for solving any quadratic equation.

1. Where the Quadratic Formula Comes From
2. Identifying a, b and c
3. Substituting Correctly
4. Simplifying the Formula
5. Two Real Solutions
6. One Repeated Solution
7. No Real Solutions

UNIT 12

The Discriminant

Predict the number and type of solutions before solving an equation.

1. Meaning of the Discriminant
2. Positive Discriminant
3. Zero Discriminant
4. Negative Discriminant
5. Connecting Discriminant and Graphs
6. Classifying Roots
7. Using the Discriminant Efficiently

UNIT 13

Complex Quadratic Solutions

Extend quadratic solutions beyond the real number system.

1. Why Imaginary Numbers Exist
2. Understanding i
3. Square Roots of Negative Numbers
4. Complex Number Basics
5. Quadratic Formula with Complex Roots
6. Conjugate Pairs
7. Checking Complex Solutions

UNIT 14

Quadratic Applications

Model motion, area, business and optimization with quadratic equations.

1. Projectile Motion
2. Maximum Height
3. Area Problems
4. Revenue and Profit
5. Optimization
6. Engineering Applications
7. Building a Quadratic Model

UNIT 15

Advanced Quadratic Problem Solving

Combine algebra, graphs and modeling to solve sophisticated quadratic problems.

1. Choosing the Best Solving Method
2. Comparing Factoring, Formula and Square Completion
3. Systems with Quadratics
4. Quadratic Inequalities
5. Intersections of Lines and Parabolas
6. Cumulative Real-World Problems
7. Quadratic Mastery Review