Algebra Basics

Algebra

Definition

• Algebra is a branch of mathematics that deals with the study of variables and their relationships, often expressed through the use of symbols, equations, and functions.

Key Concepts

• Variables: Letters or symbols that represent unknown values or quantities.
• Constants: Numbers that do not change value.
• Algebraic Expressions: Combinations of variables, constants, and mathematical operations.
• Equations: Statements that express the equality of two algebraic expressions.
• Functions: Relations between variables, often represented as f(x) =...

Operations

• Addition and Subtraction: Combining like terms and applying the distributive property.
• Multiplication and Division: Applying the rules of exponents and the order of operations (PEMDAS).
• Exponents: Rules for multiplying and dividing expressions with exponents.

Equations and Inequalities

• Linear Equations: Equations in which the highest power of the variable(s) is 1.
  • Example: 2x + 3 = 5
• Quadratic Equations: Equations in which the highest power of the variable(s) is 2.
  • Example: x^2 + 4x + 4 = 0
• Systems of Equations: Sets of two or more equations with multiple variables.
• Inequalities: Statements that express a relationship between expressions using <, >, ≤, or ≥.

Graphing

• Cartesian Coordinates: A system of graphing points on a plane using x and y axes.
• Graphs of Functions: Visual representations of functions, including linear, quadratic, and polynomial functions.

Solving Equations and Inequalities

• Substitution Method: Replacing variables with values to solve for a specific variable.
• Elimination Method: Adding or subtracting equations to eliminate a variable.
• Graphing Method: Using the intersection of graphs to solve systems of equations.
• Quadratic Formula: A formula for solving quadratic equations: x = (-b ± √(b^2 - 4ac)) / 2a.