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Questions and Answers

What is the axis of symmetry?

A statement that two algebraic expressions are equal

A numerical factor in a term

A polynomial of two terms

A line that divides a figure into two parts that are mirror images (correct)

What is a binomial?

A polynomial of two terms (correct)

A polynomial of three terms

A polynomial of four terms

A polynomial of one term

What is a coefficient?

The numerical factor in a term

Define complex conjugates.

Number pairs of the form a + bi and a - bi Signup and view all the answers

What is a complex number?

The real numbers AND the imaginary numbers Signup and view all the answers

What is meant by a constant?

A quantity whose value does not change Signup and view all the answers

What is a constant function?

A function of the form y = a where a is a real number Signup and view all the answers

Define correlation.

The strength of a relationship between two data sets Signup and view all the answers

What is a cubic function?

A polynomial function with the highest power being three Signup and view all the answers

What is an equation?

A statement that two algebraic expressions are equal Signup and view all the answers

What does it mean to evaluate an expression?

Determining the arithmetic value of an expression by substituting number values for the variables Signup and view all the answers

Define variable.

A symbol, usually a letter, that represents one or more numbers Signup and view all the answers

What is the leading coefficient?

The coefficient of the term of highest degree in a polynomial Signup and view all the answers

What is a function?

A relation in which each element in the domain corresponds with exactly one element in the range Signup and view all the answers

What is a square matrix determinant?

A real number describing the matrix determined by ad - bc in a 2x2 matrix Signup and view all the answers

Define the discriminant.

The value of the expression b^2 - 4ac for a quadratic equation Signup and view all the answers

What is an x-intercept?

A point at which a graph of a function crosses the x-axis Signup and view all the answers

What is a y-intercept?

A point at which a graph of a function crosses the y-axis Signup and view all the answers

Define transformation.

A change made to the values of a function which translates, reflects, rotates, or dilates a graph of the function Signup and view all the answers

What is a turning point?

A point where the graph of a function changes direction Signup and view all the answers

Study Notes

Algebra II Vocabulary Overview

Axis of Symmetry: Divides a figure into two mirror-image parts.
Binomial: A polynomial consisting of two distinct terms.
Coefficient: Numerical factor attached to a variable in a term.
Complex Conjugates: Pairs of numbers in the form (a + bi) and (a - bi).
Complex Number: Combination of real and imaginary numbers.
Conjugate: Pairs where the radicals or imaginary signs are opposites.
Constant: Unchanging quantity, e.g., a fixed number in an equation.
Constant Function: Represented by (y = a), where (a) is a constant real number.
Constant Term: A term in an expression without any variable.
Correlation: Measures the strength of the relationship between two data sets.
Cubic Function: Polynomial with the highest degree of three.
Degree: Highest exponent appearing in a polynomial.
Dependent Variable: Output values in a function, generally denoted as (y).
Determinant: A real number that describes the properties of a square matrix, calculated as (ad - bc) for a (2x2) matrix.
Discriminant: The expression (b^2 - 4ac) for determining the nature of roots in quadratic equations.
Domain: Set of all possible input values, usually represented as (x).
End Behavior: Describes the graph’s behavior as it moves away from the origin.
Equation: States that two algebraic expressions are equal.
Evaluate: Process of substituting number values into an expression to determine its value.
Expression: Mathematical phrase combining variables and numbers, without an equals sign.
Factor (noun): Numbers or expressions that, when multiplied, give a specific result.
Factor (verb): Rewriting an expression into its constituent factors.
Function: Relation where each input corresponds uniquely to one output.
Greatest Common Factor: The largest common factor among terms in an expression.
Horizontal: Describes lines that run parallel to the ground.
Imaginary Number: Numbers in the form (a + bi), where (b) is non-zero and (i) represents (\sqrt{-1}).
Independent Variable: Input values in a function, commonly denoted as (x).
Inequality: Relates two expressions that are not necessarily equal.
Integer: Whole numbers, both positive and negative, including zero.
Leading Coefficient: Coefficient of the term in a polynomial with the highest degree.
Linear Function: Function whose graph results in a straight line.
Matrix: Rectangular arrangement of numbers confined within brackets.
Model: Mathematical representation of real-life situations through equations or graphs.
Monomial: A polynomial consisting of a single term.
Multiplicity: Refers to how many times a linear factor appears in a polynomial’s factored form.
Nature of the Roots: Classification of roots as real, rational, or imaginary.
Non-integer: Any number that is not a whole number.
Ordered Pair: A pair of numbers used to represent a point in a coordinate plane.
Parabola: The specific curve defined by a quadratic function.
Parallel: Lines that never intersect and maintain the same slope.
Parent Function: The simplest function in a family of functions.
Perpendicular: Lines that intersect to form right angles with opposite reciprocal slopes.
Polynomial: Expression composed of variables raised to integer powers and combined through addition, subtraction, and multiplication.
Quadratic Formula: Formula for determining the roots of a quadratic equation: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}).
Quadratic Function: Written in the form (f(x) = ax^2 + bx + c), where (a) is non-zero.
Quartic Function: A polynomial function of degree four.
Quintic Function: A polynomial function of degree five.
Range: Set of all output values from a relation, often represented as (y).
Rate of Change: Change in one variable relative to another; commonly interpreted as slope.
Rational Number: Any number that can be expressed precisely as a ratio of two integers.
Real Number: Non-imaginary numbers, including all rational and irrational values.
Reflection: A transformation resulting in a graph flipped across an axis or line.
Relation: A collection of ordered pairs.
Relative Maximum: The peak value of a function at a turning point where the graph goes up to down.
Relative Minimum: The lowest value of a function at a turning point where the graph goes down to up.
Root: Any value of (x) that makes the function equal to zero ((f(x) = 0)).
Simplify: Process of reducing complexity in expressions through various methods.
Slope: Ratio indicating vertical change over horizontal change in a linear function.
Solution of a System: Set of variable values that satisfy all equations in the system.
Standard Form of a Polynomial: Arranges polynomial terms in descending order based on their degrees.
System: Collection of two or more equations using the same variables.
Transformation: Modification of function values resulting in graph translations, reflections, rotations, or dilations.
Translation: The horizontal or vertical shifting of a graph.
Trinomial: A polynomial comprising three separate terms.
Turning Point: A point marking a change in direction of a function's graph.
Variable: Symbol, typically a letter, representing one or more unknown values.
Vertex of a Parabola: The point at which a parabola reaches its highest or lowest value.
Vertical: Describes lines that are perpendicular to the horizon.
Vertical Compression: Reduction of a function’s (y)-values by a factor between 0 and 1.
Vertical Stretch: Multiplication of a function's (y)-values by a factor greater than 1.
X-Intercept: The point at which a graph intersects the (x)-axis.
Y-Intercept: The point at which a graph intersects the (y)-axis.
Zero of a Function: Any (x) value where (f(x) = 0).