Algebra Basics

What is Algebra?

• Algebra is a branch of mathematics that deals with variables and their relationships
• It involves the study of mathematical symbols and the rules for manipulating these symbols to solve equations and study structures

Basic 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
• Inequalities: Statements that express a relationship between two algebraic expressions (e.g. greater than, less than)

Operations

• Addition: Combining two or more algebraic expressions by adding corresponding terms
• Subtraction: Combining two or more algebraic expressions by subtracting corresponding terms
• Multiplication: Combining two or more algebraic expressions by multiplying corresponding terms
• Division: Dividing one algebraic expression by another

Solving Equations

• Linear Equations: Equations in which the highest power of the variable(s) is 1
• Quadratic Equations: Equations in which the highest power of the variable(s) is 2
• Factoring: Expressing an algebraic expression as a product of simpler expressions
• Quadratic Formula: A formula for solving quadratic equations: x = (-b ± √(b^2 - 4ac)) / 2a

Graphing

• Coordinate Plane: A two-dimensional plane with x-axis and y-axis
• Graph of an Equation: The set of points on a coordinate plane that satisfy an equation
• Linear Graphs: Graphs of linear equations, which are straight lines
• Quadratic Graphs: Graphs of quadratic equations, which are parabolas

Functions

• Domain: The set of input values for a function
• Range: The set of output values for a function
• Composition of Functions: Combining two or more functions to create a new function

What is Algebra?

• Algebra is a branch of mathematics that deals with variables and their relationships.
• It involves the study of mathematical symbols and the rules for manipulating these symbols to solve equations and study structures.

Basic Concepts

• Variables are letters or symbols that represent unknown values or quantities.
• Constants are numbers that do not change value.
• Algebraic expressions are combinations of variables, constants, and mathematical operations.
• Equations are statements that express the equality of two algebraic expressions.
• Inequalities are statements that express a relationship between two algebraic expressions, such as greater than or less than.

Operations

• Addition is the process of combining two or more algebraic expressions by adding corresponding terms.
• Subtraction is the process of combining two or more algebraic expressions by subtracting corresponding terms.
• Multiplication is the process of combining two or more algebraic expressions by multiplying corresponding terms.
• Division is the process of dividing one algebraic expression by another.

Solving Equations

• Linear equations are equations in which the highest power of the variable(s) is 1.
• Quadratic equations are equations in which the highest power of the variable(s) is 2.
• Factoring is the process of expressing an algebraic expression as a product of simpler expressions.
• The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, which is used to solve quadratic equations.

Graphing

• The coordinate plane is a two-dimensional plane with x-axis and y-axis.
• The graph of an equation is the set of points on a coordinate plane that satisfy an equation.
• Linear graphs are graphs of linear equations, which are straight lines.
• Quadratic graphs are graphs of quadratic equations, which are parabolas.

Functions

• The domain of a function is the set of input values for a function.
• The range of a function is the set of output values for a function.
• Composition of functions is the process of combining two or more functions to create a new function.