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Algebra 2 Vocabulary Flashcards
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Algebra 2 Vocabulary Flashcards

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@SharperEducation9982

Questions and Answers

What is an Absolute Value Equation?

  • An equation that only has constant terms
  • An equation containing an absolute value expression (correct)
  • An equation that is always negative
  • An equation without any variables

    • What does an Algebraic Expression consist of?

    A combination of variables, numbers, and at least one operation.

    Define 'Base' in mathematics.

    The number that is multiplied by itself the indicated amount of times.

    What is a Coefficient?

    <p>The number in front of the variable.</p> Signup and view all the answers

    What are Complex Conjugates?

    <p>Two complex numbers of the form a + bi and a - bi.</p> Signup and view all the answers

    What is a Complex Number?

    <p>A number of the form a + bi where a and b are real numbers.</p> Signup and view all the answers

    Define Conjugates.

    <p>The expressions a + √b and a - √b.</p> Signup and view all the answers

    What is the Constant of Variation?

    <p>The constant ratio of two variable quantities in a direct variation equation.</p> Signup and view all the answers

    What is a Constant Term?

    <p>A term without a variable but with a number.</p> Signup and view all the answers

    What does the Correlation Coefficient represent?

    <p>A measure of how accurately a line portrays a set of data.</p> Signup and view all the answers

    What is Direct Variation?

    <p>A relationship where the data increase or decrease together at a constant rate.</p> Signup and view all the answers

    Define Domain.

    <p>The set of all possible input values of a relation or function.</p> Signup and view all the answers

    What is the Elimination Method?

    <p>A method involving multiplying equations to eliminate a variable in a linear system.</p> Signup and view all the answers

    What is an Equation?

    <p>A mathematical statement that states two expressions are equal.</p> Signup and view all the answers

    Define Equation in Two Variables.

    <p>An equation that contains 2 variables.</p> Signup and view all the answers

    What are Equivalent Equations?

    <p>Equations that have the same solution(s).</p> Signup and view all the answers

    What are Equivalent Expressions?

    <p>Two algebraic expressions that have the same value for all variable(s).</p> Signup and view all the answers

    Define Exponent.

    <p>The number or variable that represents how many times the base is multiplied.</p> Signup and view all the answers

    What is an Extraneous Solution?

    <p>An apparent solution that must be rejected for not satisfying the original equation.</p> Signup and view all the answers

    What does a Formula represent?

    <p>An equation that relates two or more quantities.</p> Signup and view all the answers

    What defines a Function?

    <p>A relation where each input has exactly one output.</p> Signup and view all the answers

    What is Function Notation?

    <p>Using f(x) to represent the dependent variable of a function.</p> Signup and view all the answers

    Define Identity.

    <p>A statement that equates two equivalent expressions.</p> Signup and view all the answers

    What is an Imaginary Number?

    <p>A complex number of the form a + bi where b does not equal 0.</p> Signup and view all the answers

    Define Imaginary Unit i.

    <p>i = √-1.</p> Signup and view all the answers

    What is a Leading Coefficient?

    <p>The coefficient in the term of a polynomial function with the greatest exponent.</p> Signup and view all the answers

    Define Like Terms.

    <p>Terms that have the same variable parts raised to the same power.</p> Signup and view all the answers

    What is a Linear Function?

    <p>A function that can be written in the form y = mx + b.</p> Signup and view all the answers

    Define Linear Inequality in Two Variables.

    <p>An inequality that can be expressed in the form Ax + By.</p> Signup and view all the answers

    What is a Numerical Expression?

    <p>An expression consisting of numbers, operations, and grouping symbols.</p> Signup and view all the answers

    Define Opposite.

    <p>The additive inverse of a number.</p> Signup and view all the answers

    What is an Ordered Triple?

    <p>A set of three numbers (x,y,z) that represents a point in space.</p> Signup and view all the answers

    What is a Parabola?

    <p>The graph of a quadratic function.</p> Signup and view all the answers

    Define Parallel Lines.

    <p>Two lines in the same plane that do not intersect.</p> Signup and view all the answers

    What is a Parent Function?

    <p>The most basic function in a family of functions.</p> Signup and view all the answers

    What defines Perpendicular Lines?

    <p>Two lines that intersect to form a right angle.</p> Signup and view all the answers

    What is a Piecewise Function?

    <p>A function defined by at least two equations for different parts of its domain.</p> Signup and view all the answers

    What is Point-Slope Form?

    <p>An equation of a line written as y - y1 = m(x - x1).</p> Signup and view all the answers

    What is Power in mathematics?

    <p>An expression representing repeated multiplication of the same factor.</p> Signup and view all the answers

    What is a Pure Imaginary Number?

    <p>A complex number where a = 0 and b does not equal 0.</p> Signup and view all the answers

    What is a Quadratic Equation in One Variable?

    <p>An equation that can be expressed as ax² + bx + c.</p> Signup and view all the answers

    What is the Quadratic Formula?

    <p>A formula used to find solutions of a quadratic equation.</p> Signup and view all the answers

    Define Radicand.

    <p>The number or expression beneath the radical.</p> Signup and view all the answers

    What does Rationalizing the Denominator mean?

    <p>Eliminating a radical expression in the denominator of a fraction.</p> Signup and view all the answers

    Define Reciprocal.

    <p>The number 1/b that, when multiplied with b, equals 1.</p> Signup and view all the answers

    What is a Relation in mathematics?

    <p>A mapping or pairing of input values with output values.</p> Signup and view all the answers

    What does a Scatter Plot represent?

    <p>A graph of a set of data pairs (x,y).</p> Signup and view all the answers

    Define Slope.

    <p>Rise over run; change in y over change in x.</p> Signup and view all the answers

    What is Slope-Intercept Form?

    <p>A linear equation written as y = mx + b.</p> Signup and view all the answers

    Define Solution of a System of Linear Equations in Two Variables.

    <p>An ordered pair (x,y) satisfying each equation in the system.</p> Signup and view all the answers

    What is the Solution of a System of Linear Equations in Three Variables?

    <p>An ordered triple (x,y,z) that satisfies each equation.</p> Signup and view all the answers

    What is the Substitution Method?

    <p>A method for solving a system of equations by substituting a variable.</p> Signup and view all the answers

    Define Standard Form of a Linear Equation.

    <p>An equation in the form Ax + By = C.</p> Signup and view all the answers

    What are Terms of an Expression?

    <p>The parts of an expression that are added together.</p> Signup and view all the answers

    What is a Variable?

    <p>A letter representing one or more numbers.</p> Signup and view all the answers

    What is the Vertex of a Parabola?

    <p>The highest or lowest point of a parabola.</p> Signup and view all the answers

    Define Vertex of an Absolute Value Graph.

    <p>The highest or lowest point on an absolute value graph.</p> Signup and view all the answers

    What is an x-intercept?

    <p>The x coordinate of a point where a graph intersects the x-axis.</p> Signup and view all the answers

    Define y-intercept.

    <p>The y coordinate of a point where a graph intersects the y-axis.</p> Signup and view all the answers

    Study Notes

    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)).

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