Algebra 2 Terms Flashcards

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Questions and Answers

What is an algebraic expression?

A mathematical phrase that contains one or more variables

What are opposites in mathematics?

Two numbers that are equal distances from zero on a number line

What is the origin in a coordinate plane?

(0,0)

What is a variable?

A symbol used to represent a quantity that can change Signup and view all the answers

What is a transformation?

A change in the position, size, or shape of a figure Signup and view all the answers

What is a reflection in mathematics?

A transformation that reflects, or 'flips', a graph or figure across a line Signup and view all the answers

What is a stretch in terms of transformations?

A transformation that pulls the points of a graph horizontally or vertically away from the axes Signup and view all the answers

What is a compression in terms of transformations?

A transformation that pushes the points of a graph toward the axes Signup and view all the answers

What are like terms?

Terms that have the same variables and powers Signup and view all the answers

What is a translation in graphing?

A transformation that shifts or slides every point of a figure or graph the same distance Signup and view all the answers

What is regression?

The statistical study of the relationship between variables Signup and view all the answers

What is correlation?

A measure of the strength and direction of the relationship between two variables Signup and view all the answers

What is a line of best fit?

The line that comes closest to all of the points in a data set Signup and view all the answers

What is a correlation coefficient?

A measure of how well the data set is fit by a model Signup and view all the answers

What is a common logarithm?

A logarithm whose base is 10, denoted log10 or just log Signup and view all the answers

What is a logarithm?

The exponent that a specified base must be raised to in order to get a certain value Signup and view all the answers

What is an inverse function?

The function that results from exchanging the input and output values of a one-to-one function Signup and view all the answers

What is an inverse relation?

The inverse of the relation consisting of all ordered pairs (x,y) Signup and view all the answers

What is exponential decay?

An exponential function of the form f(x)=ab^x where a>0 and 0<b<1 Signup and view all the answers

What is an exponential function?

A function of the form f(x)=ab^x where a and b are real numbers with a≠0, b>0, and b≠1 Signup and view all the answers

What is a relation in mathematics?

A set of ordered pairs Signup and view all the answers

What is a function?

A relation in which every input is paired with exactly one output Signup and view all the answers

What is an exponent?

The number that indicates how many times the base is used as a factor Signup and view all the answers

What is standard form in quadratic functions?

ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0 Signup and view all the answers

What is vertex form of a quadratic function?

f(x) = a(x-h)^2 + k, where (h,k) is the vertex Signup and view all the answers

What is a linear equation in one variable?

An equation that can be written in the form ax = b, where a and b are constants and a ≠ 0 Signup and view all the answers

What is a root of an equation?

The value of the variable that makes the equation true Signup and view all the answers

What is the coefficient of determination?

The number R^2, with 0 ≤ R^2 ≤ 1 Signup and view all the answers

Study Notes

Algebraic Concepts and Definitions

Algebraic Expression: A mathematical phrase including variables, numbers, and operation symbols.
Opposites: Numbers that are equidistant from zero on a number line.
Origin: The point at which the x-axis and y-axis intersect, represented as (0,0).
Variable: A symbol representing a quantity that is subject to change.

Transformations and Graphical Changes

Transformation: Adjustments in a figure's position, size, or shape.
Reflection: A transformation that flips a figure across a line of reflection, keeping the same distance from the line on each side.
Stretch: A transformation that expands a graph away from the y-axis or x-axis.
Compression: A transformation that pushes the points of a graph towards the y-axis or x-axis.
Translation: A transformation that moves every point of a figure or graph the same distance in a specified direction.

Statistical Relationships

Regression: The statistical analysis of how two or more variables relate to one another.
Correlation: Indicates both the strength and direction of the relationship between two data sets.
Line of Best Fit: A line that best represents the data points in a scatter plot.

Logarithmic Concepts

Common Logarithm: A logarithm with a base of 10, commonly denoted as log10 or simply log.
Logarithm: Represents the exponent to which a specific base must be raised to achieve a given value.

Function Concepts

Inverse Function: A function created by swapping the input and output values of a one-to-one function; denoted as f^-1(x).
Inverse Relation: Created by reversing the ordered pairs (x,y); its graph is a reflection across the line y=x.
Exponential Function: Characterized by the form f(x)=ab^x, where a≠0, b>0, and b≠1.
Exponential Decay: A specific type of exponential function where the base b is less than 1, leading to a decrease over time.

Additional Algebraic Concepts

Relation: A collection of ordered pairs, showcasing connections between sets.
Function: A specific type of relation where each input corresponds to exactly one output.
Exponent: Indicates how many times the base is multiplied by itself.
Standard Form: A general form for expressing quadratic equations as ax^2 + bx + c = 0, with defined parameters for a, b, and c.
Vertex Form of a Quadratic Function: f(x)=a(x-h)^2+k, which clearly indicates the vertex at (h,k).
Linear Equation in One Variable: Formulated as ax=b, where both a and b are constants and a≠0.
Root of an Equation: The solution that satisfies the equation.
Coefficient of Determination (R²): A statistical measure representing the proportion of variance in a dependent variable predictable from the independent variable(s).

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Test your knowledge of key algebraic terms with these flashcards! Each card features a term along with its definition, helping you grasp essential concepts in Algebra 2. Perfect for review before exams or for quick study sessions.