Algebra Basics

Study Notes

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.

Variables: Letters or symbols that represent unknown values or quantities.
Constants: Numbers that do not change value.
Terms: Parts of an expression separated by addition or subtraction.
Expressions: Combinations of variables, constants, and mathematical operations.
Equations: Statements that express the equality of two expressions.
Inequalities: Statements that express a relationship between two expressions, but not necessarily equal.

Addition: Combining two or more expressions by adding their corresponding terms.
Subtraction: Combining two or more expressions by subtracting their corresponding terms.
Multiplication: Combining two or more expressions by multiplying their corresponding terms.
Division: Combining two or more expressions by dividing their corresponding terms.

Linear Equations: Equations in which the highest power of the variable is 1.
- Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
- Standard Form: ax + by = c, where a, b, and c are constants.
Quadratic Equations: Equations in which the highest power of the variable is 2.
- Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are constants.

Domain: The set of input values for which a function is defined.
Range: The set of output values that a function can produce.
Function Notation: f(x) = ..., where x is the input and f(x) is the output.
Graphing: Visual representation of a function's relationship between input and output values.

Coordinate Plane: A two-dimensional plane with x and y axes.
Graphing Linear Equations: Lines with a single slope and y-intercept.
Graphing Quadratic Equations: Parabolas with a vertex, axis of symmetry, and x-intercepts.

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Algebra studies variables and their relationships, expressed through symbols, equations, and functions.

Variables are letters or symbols representing unknown values or quantities.
Constants are numbers that do not change value.
Terms are parts of an expression separated by addition or subtraction.
Expressions are combinations of variables, constants, and mathematical operations.
Equations are statements expressing the equality of two expressions.
Inequalities are statements expressing a relationship between two expressions, but not necessarily equal.

Linear equations have a highest power of the variable of 1.
Slope-Intercept Form is y = mx + b, where m is the slope and b is the y-intercept.
Standard Form is ax + by = c, where a, b, and c are constants.

Quadratic equations have a highest power of the variable of 2.
Quadratic Formula is x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are constants.

Domain is the set of input values for which a function is defined.
Range is the set of output values that a function can produce.
Function Notation is f(x) = ..., where x is the input and f(x) is the output.
Graphing is a visual representation of a function's relationship between input and output values.

Coordinate Plane is a two-dimensional plane with x and y axes.
Graphing Linear Equations produces lines with a single slope and y-intercept.
Graphing Quadratic Equations produces parabolas with a vertex, axis of symmetry, and x-intercepts.