Algebra 101

Algebra

What is Algebra?

• Branch of mathematics that deals with variables and their relationships
• Involves the study of algebraic expressions, equations, and functions

Key Concepts:

• Variables: Letters or symbols that represent unknown values
• 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 a set of inputs (domain) and a set of possible outputs (range)

Types of Algebra:

• Elementary Algebra: Deals with solving linear equations and inequalities, graphing lines and curves, and quadratic equations
• Intermediate Algebra: Covers systems of equations, functions, and graphing
• College Algebra: Includes advanced topics such as polynomial and rational functions, conic sections, and sequences and series

Algebraic Operations:

• Addition and Subtraction: Combine like terms by adding or subtracting coefficients
• Multiplication: Distribute numbers and variables to multiply algebraic expressions
• Division: Divide coefficients and variables to simplify expressions

Solving Equations:

• Linear Equations: Equations of the form ax + by = c, where a, b, and c are constants
• Quadratic Equations: Equations of the form ax^2 + bx + c = 0, where a, b, and c are constants
• Systems of Equations: Sets of two or more equations with variables

Graphing:

• Cartesian Coordinates: Plot points on a grid using x and y axes
• Graphing Linear Equations: Plot lines on a graph to visualize relationships between variables
• Graphing Quadratic Equations: Plot parabolas to visualize relationships between variables