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Questions and Answers
What is the highest power of the variable in a quadratic equation?
What is the highest power of the variable in a quadratic equation?
What is the purpose of graphing an equation on a coordinate plane?
What is the purpose of graphing an equation on a coordinate plane?
What is an example of an inequality?
What is an example of an inequality?
What is the method of solving equations by finding common factors?
What is the method of solving equations by finding common factors?
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What is the notation for a function?
What is the notation for a function?
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What is the definition of a polynomial?
What is the definition of a polynomial?
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What is the method of solving systems of equations by replacing one equation with the expression from another equation?
What is the method of solving systems of equations by replacing one equation with the expression from another equation?
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What is the purpose of variables in algebra?
What is the purpose of variables in algebra?
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Study Notes
Algebra
What is Algebra?
- A branch of mathematics that deals with the study of variables and their relationships
- Uses symbols, equations, and formulas to solve problems
Key Concepts:
Variables and Expressions
- Variables: letters or symbols that represent unknown values
- Expressions: combinations of variables, constants, and mathematical operations
- Example: 2x + 5 is an expression, where x is a variable and 2 and 5 are constants
Equations and Inequalities
- Equations: statements that two expressions are equal
- Inequalities: statements that one expression is greater than, less than, or equal to another
- Examples:
- Equation: 2x + 3 = 5
- Inequality: 2x - 4 > 3
Solving Equations and Inequalities
- Linear equations: equations in which the highest power of the variable is 1
- Quadratic equations: equations in which the highest power of the variable is 2
- Methods for solving equations:
- Addition/Subtraction
- Multiplication/Division
- Factoring
- Quadratic Formula
Graphing
- Graphing equations on a coordinate plane
- x-axis: horizontal axis
- y-axis: vertical axis
- Points on the graph represent solutions to the equation
- Example: graphing the equation y = 2x - 3
Functions
- Relations between a set of inputs (domain) and a set of possible outputs (range)
- Notation: f(x) = output
- Example: f(x) = 2x + 1, where x is the input and 2x + 1 is the output
Systems of Equations
- Sets of two or more equations that must be true at the same time
- Methods for solving systems:
- Substitution
- Elimination
- Graphing
Polynomials
- Expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication
- Examples: x^2 + 3x - 4, 2x^3 - 5x^2 + x - 1
Algebra
Definition and Scope
- Algebra is a branch of mathematics that studies variables and their relationships
- It uses symbols, equations, and formulas to solve problems
Variables and Expressions
- Variables represent unknown values and are denoted by letters or symbols
- Expressions are combinations of variables, constants, and mathematical operations
- Example: 2x + 5 is an expression, where x is a variable and 2 and 5 are constants
Equations and Inequalities
- Equations are statements that two expressions are equal
- Inequalities are statements that one expression is greater than, less than, or equal to another
- Examples:
- Equation: 2x + 3 = 5
- Inequality: 2x - 4 > 3
Solving Equations and Inequalities
- Linear equations have the highest power of the variable as 1
- Quadratic equations have the highest power of the variable as 2
- Methods for solving equations include:
- Addition/Subtraction
- Multiplication/Division
- Factoring
- Quadratic Formula
Graphing
- Graphing equations on a coordinate plane with x-axis (horizontal) and y-axis (vertical)
- Points on the graph represent solutions to the equation
- Example: graphing the equation y = 2x - 3
Functions
- Relations between a set of inputs (domain) and a set of possible outputs (range)
- Notation: f(x) = output
- Example: f(x) = 2x + 1, where x is the input and 2x + 1 is the output
Systems of Equations
- Sets of two or more equations that must be true at the same time
- Methods for solving systems include:
- Substitution
- Elimination
- Graphing
Polynomials
- Expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication
- Examples: x^2 + 3x - 4, 2x^3 - 5x^2 + x - 1
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Description
Get familiar with the fundamentals of algebra, including variables, expressions, equations, and inequalities. Learn how to solve problems using symbols, equations, and formulas.
