Algebra II Vocabulary Flashcards

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Questions and Answers

What is a complex number?

A number greater than zero

A number with a real part only

A number that consists of both real (a) and imaginary (bi) parts (correct)

A negative number

What is the absolute value?

The distance between a number and zero.

Define an expression in mathematics.

A representation of a quantity that may contain numbers, variables, or operation symbols.

What is a variable?

A quantity that may change within the context of a mathematical problem or experiment. Signup and view all the answers

What is a term in mathematics?

Either a single number or variable, or numbers and variables multiplied together. Signup and view all the answers

Define a polynomial.

The general term for algebraic expressions such as monomials, binomials, and trinomials. Signup and view all the answers

What does the degree of a polynomial refer to?

The largest exponent or the largest sum of exponents of a term within a polynomial. Signup and view all the answers

What is the leading coefficient?

The coefficient of the first term of a polynomial written in descending order of exponents. Signup and view all the answers

What are the factors of a monomial?

The number(s) and/or variable(s) that are multiplied together to form a monomial. Signup and view all the answers

What is a prime polynomial?

A polynomial that cannot be factored into a product of lesser degree polynomial factors. Signup and view all the answers

If $ab = 0$, then $a = 0$ or $b = 0$.

True (A) Signup and view all the answers

What are zeros in a function?

The values of x where the function is equal to zero. Signup and view all the answers

What are x-intercepts?

Where the graph crosses the x-axis and where $f(x) = 0$. Signup and view all the answers

What is a vertical line represented by?

x = a (where a can be any real number); always has an undefined slope. Signup and view all the answers

What is a horizontal line represented by?

y = c (where c can be any real number); always has a zero slope. Signup and view all the answers

Define an inequality.

An algebraic sentence comparing two quantities. Signup and view all the answers

What is the domain of a function?

The set of all possible values of the independent variable. Signup and view all the answers

What is the range of a function?

The set of all possible values of the dependent variable. Signup and view all the answers

What is function notation?

f(x) is read as 'the value of f at x' or 'f of x'; other letters can be used to name functions. Signup and view all the answers

What represents direct variation?

y = kx where k is the constant of variation. Signup and view all the answers

Define inverse variation.

k = xy where k is the constant of variation. Signup and view all the answers

What does joint variation represent?

y = kxz where k is the constant of variation; one variable depends on two or more other variables. Signup and view all the answers

Define an arithmetic sequence.

A sequence of numbers that has a common difference between every two consecutive terms. Signup and view all the answers

What is a geometric sequence?

A sequence of numbers where each term after the first is obtained by multiplying the previous term by a constant ratio. Signup and view all the answers

Define a permutation.

An ordered arrangement of a group of objects. Signup and view all the answers

What is a combination?

The number of possible ways to select or arrange objects when there is no repetition and order does not matter. Signup and view all the answers

Define a z-score.

The number of standard deviations an element is away from the mean. Signup and view all the answers

What is a literal equation?

A formula or equation that consists primarily of variables. Signup and view all the answers

What is the standard form of a quadratic equation?

ax² + bx + c = 0 Signup and view all the answers

What is the vertex of a quadratic function?

Given standard form: (-b/2a, f(-b/2a)); Given vertex form: (h, k). Signup and view all the answers

What does the quadratic formula do?

Used to find the solutions to any quadratic equation written in standard form. Signup and view all the answers

What are increasing/decreasing intervals?

A function can be described as increasing, decreasing, or constant over a specified interval or the entire domain. Signup and view all the answers

What are extrema in a function?

The largest (maximum) and smallest (minimum) value of a function within a given interval or on the entire domain. Signup and view all the answers

Define end behavior in terms of functions.

The value of a function as x approaches positive or negative infinity. Signup and view all the answers

What is the linear parent function?

f(x) = x Signup and view all the answers

What is the quadratic parent function?

f(x) = x² Signup and view all the answers

Define the absolute value parent function.

f(x) = |x| Signup and view all the answers

What is the square root parent function?

f(x) = √x Signup and view all the answers

What is the cubic parent function?

f(x) = x³ Signup and view all the answers

Define the cube root function.

f(x) = ³√x Signup and view all the answers

What is the rational parent function?

f(x) = 1/x; the reciprocal of a linear function. Signup and view all the answers

What does the exponential growth parent function represent?

f(n) = bⁿ where b > 1. Signup and view all the answers

What is the logarithmic parent function?

f(x) = logₙ(x) where n > 1. Signup and view all the answers

What does translation of a parent function involve?

f(x - h) + k; any parent function can be shifted horizontally h units or vertically k units. Signup and view all the answers

What does dilation of a parent function refer to?

a·f(x) or f(ax); any parent function can be stretched or compressed either vertically or horizontally. Signup and view all the answers

Define reflection of a parent function.

-f(x) or f(-x); any parent function can be flipped over either axis. Signup and view all the answers

What is the inverse of a function?

Graphically, the reflection of the original graph over the line, y = x. Signup and view all the answers

Define continuity in functions.

A function that is continuous at every point in its domain. Signup and view all the answers

What is an asymptote?

A line that continually approaches a given curve but does not meet it at any finite distance. Signup and view all the answers

Define a hole in graphing functions.

Exists on the graph of a rational function at any input value causing both the numerator and denominator to be equal to zero. Signup and view all the answers

What is the fundamental counting principle?

If there are m ways for one event to occur and n ways for a second event to occur, then there are $m imes n$ ways for both events to occur. Signup and view all the answers

What is the permutation formula?

nPr(n, r) Signup and view all the answers

What is the combination formula?

nCr(n, r) Signup and view all the answers

What does ∑ (capital sigma) represent?

A summation symbol. Signup and view all the answers

Define the empirical rule in statistics.

68-95-99.7 rule; approximate percentage of element distribution. Signup and view all the answers

Study Notes

Complex Numbers and Absolute Value

A complex number is represented as a ± bi, combining real (a) and imaginary (bi) parts.
Absolute value reflects the distance of a number from zero on the number line.

Algebraic Concepts

An expression constitutes numbers, variables, and operation symbols.
Variables, like x or y, represent quantities that can adjust in mathematical scenarios.
Terms can be a single number/variable or a product of both, separated by addition or subtraction.

Polynomials and Their Characteristics

Polynomials encompass algebraic expressions such as monomials, binomials, and trinomials.
The degree of a polynomial is defined by the largest exponent or sum of exponents in its terms.
The leading coefficient is the coefficient of the first term when written in decreasing order of exponents.

Functions and Graphs

Zeros of a function indicate where the function equals zero (f(x) = 0).
X-intercepts occur where the graph crosses the x-axis.
Vertical lines have an equation x = a with undefined slopes; horizontal lines are y = c with a zero slope.

Relationships and Variations

Inequalities compare two quantities in algebraic sentences.
Domain refers to all possible values that an independent variable can take.
Range represents all possible values of a dependent variable.

Variations Defined

Direct variation follows the formula y = kx, indicating a constant ratio between x and y.
Inverse variation is expressed as k = xy, indicating a constant product relationship.
Joint variation presents y = kxz, where one variable depends on two or more others.

Sequences and Combinatorics

An arithmetic sequence has a consistent difference between consecutive terms.
A geometric sequence involves multiplying each term by a constant ratio.
Permutations are ordered arrangements; combinations involve selection without regard to order.

Statistical Measures

Z-score indicates how many standard deviations an element is from the mean.
Literal equations predominantly consist of variables, often used to express relationships.

Quadratic Functions

Standard form for quadratic equations is ax² + bx + c = 0.
Vertex of a quadratic function can be found using special formulas based on its standard and vertex forms.
The quadratic formula x = -b ± √(b² - 4ac)/2a solves quadratic equations.

Function Behavior

Increasing/decreasing intervals characterize the behavior of functions over specified ranges.
Extrema denote the maximum and minimum values of functions, either locally or globally.
End behavior describes the function's value as x approaches positive or negative infinity.

Parent Functions

Parent functions represent the simplest forms:
- Linear: f(x) = x
- Quadratic: f(x) = x²
- Absolute Value: f(x) = |x|
- Square Root: f(x) = √x
- Cubic: f(x) = x³
- Cube Root: f(x) = ³√x
- Rational: f(x) = 1/x
- Exponential Growth: f(n) = bⁿ (b > 1)
- Logarithmic: f(x) = logₙ(x) (n > 1)

Transformations and Inverses

Translations of parent functions shift graphs horizontally/vertically.
Dilations stretch or compress graphs either vertically or horizontally.
Reflections flip graphs over axes, altering their orientations.

Continuity and Discontinuities

Continuity indicates a function is unbroken at all points in its domain.
Asymptotes are lines that approach a curve but do not intersect it, indicating discontinuity.
Holes in functions occur where both the numerator and denominator are zero, causing discontinuity.

Counting Principles

Fundamental counting principle: If there are m ways for one event and n ways for another, there are m ∙ n ways for both.
Permutations and combinations have specific formulas: nPr for permutations and nCr for combinations.

Statistical Distribution

The empirical rule (68-95-99.7 rule) describes the distribution of elements in a normal distribution curve.

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Description

Test your understanding of key terms in Algebra II with these flashcards. Each card includes a word and its definition to enhance your vocabulary. Ideal for students preparing for the Virginia SOL exams.