Algebra Concepts and Functions

Algebra Concepts

• Slope Intercept Equation: Defined by the formula (y = mx + b), where (m) is the slope and (b) is the y-intercept.
• Perfect Square: Result from multiplying a number by itself.
• Inequality Symbol: Indicates greater than (>) or less than (<).
• Constant: A value that remains unchanged.
• Intersect: Point where lines meet in the context of a system of equations.

Mathematical Functions and Terms

• Square Root: The number that, when multiplied by itself, yields a given product.
• Vertical Line Test: A method to determine if a relation qualifies as a function by checking if any vertical line intersects the graph at more than one point.
• Inverse Operations: Operations that cancel each other out (e.g., addition and subtraction).
• System of Equations: Composed of two or more equations to solve simultaneously.
• Negative Exponent: Indicates the reciprocal of the base raised to the corresponding positive exponent.

Graphing Inequalities

• Closed Circle: Used in graphing when an inequality includes equality (≥ or ≤).
• Dotted Line: Represents inequalities that exclude equality ( (> ) or (<)).
• Solid Line: Indicates that the inequality includes equality in graphing.

Problem Solving Techniques

• FOIL Method: Acronym for First, Outside, Inside, Last; a technique for multiplying two binomials.
• Solutions: Values that satisfy an equation.
• Elimination and Substitution: Two primary methods for solving systems of equations.

Types of Numbers and Operations

• Monomial: A single term expression.
• Polynomial: Composed of one or more terms, connected by addition or subtraction.
• Coefficient: A number that multiplies a variable.
• Reciprocal: An inverted form of a fraction.
• Exponent: Indicates the number of times a base is multiplied by itself.

Lines and Angles

• Slope: Measures the steepness of a line; calculated as rise over run.
• Y-intercept: The point where a line crosses the y-axis.
• Hypotenuse: The longest side of a right triangle, opposite the right angle.
• Zero and Undefined Slopes: Zero slope refers to horizontal lines; undefined slope refers to vertical lines.

Algebraic Identities and Properties

• Identity: Equations that hold true for every possible variable value.
• Greatest Common Factor (GCF): The largest number that divides a set of numbers evenly.
• Least Common Multiple (LCM): The smallest number that is a multiple of given numbers.

Additional Concepts

• Rise/Run: Provides a way to calculate slope based on vertical and horizontal movement between two points.
• Trinomial and Binomial: A trinomial has three terms, while a binomial has two, both connected by addition or subtraction.
• Pythagorean Theorem: Relates the sides of a right triangle through the formula (c^2 = a^2 + b^2).