# Algebra Definitions

Browse our growing collection of algebra definitions:

## ARC

ARC an abbreviation of average rate of change is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value (Δy) divided by the change in the x-value (Δx) for two distinct points on the graph.

## Abscissa

In mathematics, the abscissa and the ordinate are respectively the first and second coordinates of a point in a coordinate system. The abscissa is the first coordinate in an ordered pair and the ordinate is the second coordinate.

## Absolute Value

The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign.

## Accuracy

Accuracy is how close an approximation is to an actual value. In other terms, in measurement of a set, accuracy refers to closeness of the measurements to a specific value, while precision refers to the closeness of the measurements to each other.

## Argand Plane

The argand plane otherwise known as the complex plane, z-plane or gauss plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

## Average Rate of Change

Average rate of change or ARC is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value (Δy) divided by the change in the x-value (Δx) for two distinct points on the graph.

## Bidimensional Space

Bidimensional space otherwise referred to as two dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (a point).

## Complex Plane

The complex plane otherwise known as the argand plane, z-plane or gauss plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

## Compression

A compression or contraction is a transformation in which a figure grows smaller. Compressions may be with respect to a point (compression of a geometric figure) or with respect to the axis of a graph (compression of a graph).

## Delta (Δ, δ)

Delta (Δ, δ) is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4.

## Horizontal Dilation

A horizontal dilation or stretch is a stretch in which a plane figure is distorted horizontally.

## Horizontal Stretch

A horizontal stretch or dilation is a stretch in which a plane figure is distorted horizontally.

## Leading Coefficient

A leading coefficient is the coefficient of a polynomials leading term. For instance, given the polynomial 8x^{5} + 3x^{2} - 3x + 7, the leading coefficient is 8.

## Ordinate

In mathematics, the ordinate and abscissa are respectively the second and first coordinates of a point in a coordinate system. The ordinate is the second coordinate in an ordered pair and the abscissa is the first coordinate.

## Phi (Φ, φ)

Phi (Φ, φ) is the 21st letter of the Greek alphabet. In the system of traditional Greek numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ).

## Sigma (Σ, σ)

Sigma (Σ, σ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation.

## Tau (Τ, τ)

Tau (Τ, τ) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.

## Term

A term in mathematics is a variable, constant, or the result of acting on variables and constants by function symbols. In simpler terms, terms are parts of an expression or series separated by addition or subtraction signs, or the parts of a sequence separated by commas.

## Trinomial

A trinomial is a polynomial consisting of three terms or monomials which are not like terms. Examples of trinomials include: x^{2} + 4x - 6, 4x^{5} - 3x^{4} + x^{3}, and a^{2}b + 6x + c.

## Triple Root

A triple root is a root of a polynomial equation with a multiplicity of 3. Triple root also refers to a zero of a polynomial function with multiplicity 3.

## Trivial

Trivial is related to or being the mathematically most simple case. More generally, the term trivial is used to describe any result which requires little or no effort to derive or prove.

## Two Dimensional

Two dimensional or two dimensions is the property of a plane that indicates that motion can take place in two perpendicular directions.

## Two Dimensional Space

Two dimensional space otherwise referred to as bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (a point).

## Two Dimensions

Two dimensions or two dimensional is the property of a plane that indicates that motion can take place in two perpendicular directions.

## Two Intercept Form For The Equation of a Line

Two intercept form for the equation of a line is an equation of a line where ^{x}⁄_{a} + ^{y}⁄_{b} = 1, where a is the x-intercept and b is the y-intercept.

## Undefined Slope

Undefined slope occurs when the slope is for a vertical line. A vertical line has an undefined slope because all points on the line have the same x-coordinate.

## Underdetermined System of Equations

Underdetermined system of equations is a system of linear equations or a system of polynomial equations if there are fewer equations than variables (in contrast to an overdetermined system of equations, where there are more equations than variables).

## Variable

In mathematics, a variable is a symbol used to represent an arbitrary element that can change or that may take on different values.

## Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

## Verify a Solution

Verifying or checking a solution is the process of making sure a solution is correct by making sure it satisfies any and all equations and or inequalities in a problem.

## Vertex

A vertex is a special point of a mathematical object and is usually a location where two or more lines or edges meet. In other terms, a vertex is a corner point of a geometric figure.

## Vertex of a Hyperbola

The vertices of a hyperbola are the points at which a hyperbola makes its sharpest turns. The vertices are on the major axis which is the line through the foci.

## Vertex of a Parabola

The vertex of a parabola is the point at which a parabola makes its sharpest turn. The vertex is halfway between the directrix and the focus.

## Vertex of an Ellipse

The vertices of an ellipse are the points at which an ellipse makes its sharpest turns. The vertices are on the major axis which is the line through the foci.

## Vertical Compression

A vertical compression or shrink is a compression in which a plane figure is distorted vertically.

## Vertical Dilation

A vertical dilation or stretch is a stretch in which a plane figure is distorted vertically.

## Vertical Ellipse

A vertical ellipse is a conic section which is essentially a vertically stretched circle. In more formal terms an ellipse means for two given points, the foci, an ellipse is the locus of points such that the sum of the distance to each focus is constant.

## Vertical Line Equation

The equation of a vertical line is x = k, where a represents the x-intercept.

## Vertical Line Test

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

## Vertical Parabola

A vertical parabola is a u-shaped curve with certain properties. In particular a vertical parabola is a parabola that opens either upwards or downwards.

## Vertical Reflection

A vertical reflection is a reflection in which a plane figure flips over vertically. A vertical reflection has a horizontal axis of reflection.

## Vertical Shift

In geometry, a vertical shift otherwise known as vertical translation, is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.

## Vertical Shrink

A vertical shrink or compression is a shrink in which a plane figure is distorted vertically.

## Vertical Stretch

A vertical stretch or dilation is a stretch in which a plane figure is distorted vertically.

## Vertical Translation

In geometry, a vertical translation otherwise known as vertical shift, is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.

## Vertices of a Hyperbola

The vertices of a hyperbola are the points at which a hyperbola makes its sharpest turns. The vertices are on the major axis which is the line through the foci.

## Vertices of an Ellipse

The vertices of an ellipse are the points at which an ellipse makes its sharpest turns. The vertices are on the major axis which is the line through the foci.

## Weighted Average

The weighted average or weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead it is used in computing a kind of arithmetic mean of a set of numbers in which some elements of the set carry more importance (weight, frequency, or relative importance) than others.

## X-Intercept

A point at which a graph intersects with the x-axis. The x-intercepts of a function must be real numbers, unlike roots and zeros of a function.

## Y-Intercept

A point at which a graph intersects the y-axis.

## Zero Matrix

A zero matrix is an m x n matrix where all of its elements are equal to zero and denoted by _{0}. Zero matrices are sometimes also referred to as null matrices.

## Zero Slope

A slope of zero means that the line is a horizontal line. A horizontal line has slope of 0 because all of its points have the same y-coordinate.

## Zero of a Function

A value of x which makes a function f(x) equal zero. In other terms a value of x such that f(x) = 0. A zero of a function may be a real or complex number.