Algebra 2 Vocabulary Flashcards

Algebra 2 Vocabulary

• Absolute Value Equation: Contains an absolute value expression; graphs as a V shape.

• Algebraic Expression: Comprises variables, numbers, and operations (e.g., 2x + 2).

• Base: A number multiplied by itself a specific number of times; e.g., in 4², 4 is the base.

• Coefficient: A number in front of a variable; e.g., 3 in 3x.

• Complex Conjugates: Two complex numbers in the form a + bi and a - bi (e.g., 3 - 4i and 3 + 4i).

• Complex Number: Written as a + bi, where a and b are real numbers; i represents the square root of -1 (e.g., 3 + 8i).

• Conjugates: Expressions like a + √b and a - √b, useful for rationalizing denominators; their product is rational (e.g., 2 + √6 and 2 - √6).

• Constant of Variation: In direct variation equations, it represents the constant ratio of two variable quantities (e.g., 6 in y = 6x).

• Constant Term: A numeric term without a variable (e.g., 4 in 3x + 4 = 2).

• Correlation Coefficient: Denoted by r, ranges from -1 to 1; indicates how well a line fits a data set (e.g., r = 0.89 for 89% accuracy).

• Direct Variation: Describes a relationship where two variables change at a constant rate; y = ak, where k ≠ 0 (e.g., 2 = a × 8).

• Domain: Set of all possible input values in a function; the first number in an ordered pair (e.g., domain: {x=2,6,8,10}).

• Elimination Method: A technique for solving linear systems by eliminating a variable through addition after manipulating equations (e.g., obtain 7x = 21).

• Equation: A mathematical statement asserting the equality of two expressions; must include an equals sign (e.g., 3 + 2x = 13).

• Equation in Two Variables: Contains two variables; expressed as (e.g., 2x + 4y = 99).

• Equivalent Equations: Equations with the same solution (e.g., x + 3 = 9 and 10x = 60).

• Equivalent Expressions: Algebraic expressions that yield the same value for all variable inputs (e.g., 8x + 8x = 16x).

• Equivalent Inequalities: Inequalities with identical solutions.

• Exponent: Indicates the number of times a base is multiplied by itself (e.g., 2 in 4²).

• Extraneous Solution: A solution that does not satisfy the original equation (e.g., -3/4 in |x + 4| = 2x).

• Formula: An equation relating two or more quantities usually represented by variables (e.g., d = rt).

• Function: A relation where each input has a single output, adhering to the vertical line test (e.g., (2,5), (3,4)).

• Function Notation: Uses f(x) to denote the output of a function (e.g., f(x) = 3x + 4).

• Identity: An equation that is always true; both sides yield the same value (e.g., 3 = 3).

• Imaginary Number: A complex number where the imaginary part is non-zero (e.g., 2 + 4i).

• Imaginary Unit i: Represents √-1; i² equals -1.

• Leading Coefficient: The coefficient with the highest exponent in a polynomial (e.g., 4 in 4x²).

• Like Terms: Terms sharing the same variable parts and can be combined (e.g., 4y and 2y).

• Linear Function: Can be expressed in the form y = mx + b; graphs as a straight line (e.g., y = 4x - 2).

• Linear Inequality in Two Variables: An inequality that can be expressed in the form Ax + By < C.

• Numerical Expression: Consists only of numbers and operations, not including variables (e.g., 2 + 6 + 2(-1)).

• Opposite: The additive inverse of a number; numbers equidistant from zero on a number line.

• Ordered Triple: Represents a point in three-dimensional space in the form (x, y, z) (e.g., (4, 1, 8)).

• Parabola: The graph of a quadratic function; U-shaped.

• Parallel Lines: Lines that do not intersect and share the same slope (e.g., y = 2x + 4 and y = 2x).

• Parent Function: The simplest form of function within a family (e.g., y = x or y = |x|).

• Perpendicular Lines: Lines intersecting at a right angle; slopes are negative reciprocals (e.g., y = 4x + 8 and y = -1/4x + 6).

• Piecewise Function: Defined by multiple equations for different parts of its domain (e.g., y = {3 if x > 2 and 0 if x = 1}).

• Point-Slope Form: Written as y - y₁ = m(x - x₁); describes a line in terms of slope and a point (e.g., y - 2 = 3(x + 2)).

• Power: Represents repeated multiplication of a base (e.g., 8 in 2⁴ = 2 x 2 x 2 x 2).

• Pure Imaginary Number: Complex numbers where the real part is zero and the imaginary part is non-zero (e.g., 2i).

• Quadratic Equation in One Variable: Written in the form ax² + bx + c where a ≠ 0 (e.g., 2x² + 4x - 6).

• Quadratic Formula: Used to find solutions of the quadratic equation (e.g., x = (-b ± √(b² - 4ac)) / (2a)).

• Radicand: The expression or number beneath a radical (e.g., 4x² in √4x²).

• Rationalizing the Denominator: The process of eliminating a radical from the denominator of a fraction (e.g., rationalize √2/√4).

• Reciprocal: A number that, when multiplied by the original, equals 1 (e.g., changing 4/6 to 6/4).

• Relation: Mapping of input values to output values; can be illustrated in various forms (e.g., scatter plots).

• Scatter Plot: Graphing method for measuring the relationship between two variables through (x, y) data pairs.

• Slope: The ratio of vertical change to horizontal change; calculated as rise over run (e.g., from points (1,2) to (4,8), slope m = 2).

• Slope-Intercept Form: Linear equation expressed as y = mx + b, where m is the slope and b is the y-intercept (e.g., y = 2x - 7).

• Solution of a System of Linear Equations in Two Variables: An ordered pair satisfying all equations in the system (e.g., (1.5, 6) for y = 2x + 3).

• Solution of a System of Linear Equations in Three Variables: An ordered triple making each equation true (e.g., (2, 2, 0) for y = x and y = x + z).

• Substitution Method: Solving systems by substituting one variable's expression into another; isolates one variable (e.g., y = -2x + 5).

• Standard Form of a Linear Equation: Written as Ax + By = C, where both A and B are non-zero (e.g., 2x + 5y = 18).

• Terms of an Expression: Each component that can be added together; includes coefficients, variables, and constants (e.g., 3x², 2x, -11).

• Variable: A symbol representing one or more numbers (e.g., x in 2x + 4).

• Vertex of a Parabola: The highest or lowest point on a parabola, determined by x = -b/2a.

• Vertex of an Absolute Value Graph: The peak or trough of the graph, denoted as (h, k).

• x-intercept: The x-coordinate where a graph intersects the x-axis (e.g., (x, 0)).

• y-intercept: The y-coordinate where a graph intersects the y-axis (e.g., (0, y)).

Test your knowledge of essential algebra 2 vocabulary with these flashcards. Each card features a key term, its definition, and an example to help solidify your understanding. Perfect for preparing for quizzes or reviewing core concepts!