- absolute value
- the distance from the number to zero on a number line

Example: |3| = 3 or |-3| = 3 - absolute value function
- a function written in the vertex form
, where**f(x) = a |x – h| + k***a*≠ 0; the graph of an absolute value function is a “V” shape - asymptote
- a line that a curved graph gets closer to without every touching
- at least
- must be more than
- axis of symmetry
- for a quadratic function, a vertical line that includes the vertex of a quadratic function resulting in the two sides of the graph look like mirror images of each other
- base
- in a logarithm, the base is the number that is raised to a power

If nx = a, the logarithm of a, n is the base. - binomial
- a polynomial with two terms

Examples: (*x*- 2) or (3*x*+ 5) - change of base formula
- To change a logarithmic expression with base
*b*to a common log (base 10), use the formula:log

_{b}(ARGUMENT) = log (ARGUMENT) log*b* - circle
- the locus of points that are a fixed distance from a given point
- coefficient
- the number multiplied times a product of variables or powers of variables in a term
- compensate
- the act of making equal
- completing the square
- a method of symbolic manipulation in which a polynomial can be rewritten to include a binomial that is squared
- complex number
- a number of the form
*a + bi*where*a*and*b*are real numbers, and*b*≠ 0 - compounded monthly
- when interest is earned not only on the original principal but also on the accumulated interest of prior months
- compression
- a transformation that pushes the points of a graph vertically toward the x-axis
- congruent
- having the same size and same shape
- conjugate axis
- the line through the center of the hyperbola that is perpendicular to the line through the foci
- constant
- a term or expression with no variables; a value that does not change
- continuous
- a set of points without breaks
- critical attribute
- characteristics of a quadratic function that set it apart from others, including: x-intercepts, y-intercepts, vertex, and the axis of symmetry
- decreasing
- denotes the direction in a parabola, the y-coordinates are decreasing while the x-coordinates are increasing
- degree
- the highest exponent in an equation
- dependent variable
- a variable (usually “
*y*”) whose value is found by using the value of the independent variable (usually “*x*”) - depreciates
- losing value over time
- dimensions of a matrix
- When listing the dimensions of a matrix, give the number of rows followed by the number of columns.
- direct variation
- a relationship in which the ratio between two variables is constant

Ifor**k =***y**x*, where**y = kx**is a non-zero constant, then**k***y*varies directly with.**x** - discontinuities
- places on the graph of a function where two pieces are separated by a jump, hole, or an asymptote
- discrete
- a set of individual points
- distributive property
- a property of real numbers that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products

x(a + b) = ax + bx - domain
- the set of input values of a function or relation
- elimination
- the act of adding two equations of a system together in such a way that one of the variables is removed or eliminated from the resulting equation
- ellipse
- a closed, symmetric curve shaped like an oval, which can be formed by intersecting a cone with a plane that is not parallel or perpendicular to the cone's base

The set of points for which the sum of the distances to two foci within the curve are congruent. - equa
- the same value
- equation
- a mathematical sentence that equates two expressions; an equation contains an equal sign, =
- exponent
- says how many times to use the number in a multiplication

In this example:**8**or^{2}= 8 × 8 = 64*x*^{2}=*x*×*x* - exponential
- a function where the variable is the exponent of a constant base
- exponential decay
- for
*f*(*x*) =*a***B*^{x+c}+*d*, if*a*> 0 and 0 <*B*< 1, then the*y*-values decrease (or decay) as the*x*-values increase

The rate of decay is proportional to the*y*-value, so as the*y*-values get smaller, the graph flattens out (or approaches a horizontal asymptote). - exponential growth
- for
*f*(*x*) =*a***B*^{x+c}+*d*, if*a*> 0 and*B*> 1, then the*y*-values increase (or grow) as the*x*-values increase

The rate of decay is proportional to the*y*-value, so as the*y*-values get larger, the graph grows without bound (or exponentially). - expression
- a mathematical sentence that shows a relationship among real numbers and variables; an expression does not contain a symbol implying equality or inequality
- extraneous roots
- a solution of a modified equation that is NOT a solution to the original equation
- dxtraneous solution
- answer that must be discarded because of a domain restriction or similar problem
- focal radius
- distance from the center of a hyperbola to each focal point along the major axis
- focus
- a fixed point on the interior of a parabola

The distance from the focus to the parabola is equal to the distance from the directrix to the parabola. - formulate
- to develop or create a formula or equation
- function
- a relation that matches each element in the domain with exactly one element of the range
- holes
- points where the graph of a function does not exist
- horizontal asymptote
- a
- horizontal shift
- movement of a graph to the right or left

A function*f(x)*can be moved “*h*” units right/left by performing the operation*f*(*x*±*h*). - hyperbola
- a plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone

It is the locus of points for which the difference of the distances from two given points is a constant. - identity matrix
- a square matrix with a diagonal of 1's and the remaining elements are 0's
- imaginary number
- a value that includes the square root of a negative number
- imaginary root
- A quadratic equation is said to have imaginary roots when the quadratic formula yields imaginary or non-real answers. Also, the graph of a function with imaginary roots will not touch the x-axis.
- increasing
- denotes the direction in a parabola, the y-coordinates are increasing while the x-coordinates are increasing
- independent variable
- the input of a function (usually “
*x*”) whose value is used to find the value of the dependent variable (usually “*y*”), values can be freely chosen - index of a radical
- the
*n*th root of x where*n*is the index is represented by the radical; radical √*x*has an index of 2 and is often called the square root of*x* - inequality
- a number sentence where one quantity can be greater or less than another quantity, a number sentences with inequality symbols
- infinitely many solutions
- a system in which there are an infinite number of ordered pairs that satisfy all of the equations; also referred to as a
**dependent system** - infinite
- an unlimited number
- infinity
- going on forever, of not having an end, of having no boundary
- integer
- the set of positive and negative whole numbers {…-2, -1, 0, 1, 2 …}
- integral
- in the form of an integer (positive and negative whole numbers)
- inverse
- a function that undoes what the original function did
- inverse of a function
- a function obtained by exchanging the input and output values of a one-to-one function
- inverse of a matrix
- a second matrix that, when multiplied by the first matrix, will always result in the
**identity matrix** - inverse variation
- a relationship in which the product of two variables is constant

Ifor .**xy = k**where**y =***k**x*is a non-zero constant, then**k**varies inversely with**y**.**x** - irrational number
- a number that
**cannot**be written in fractional form, a non-terminating (does not end) and non-repeating decimal value, examples include all non-perfect square roots (√2, √3, etc. and π) - isolate
- get something by itself
- line of best fit (or "trend" line)
- a straight line that best represents the data on a scatter plot; may pass through some of the points, none of the points, or all of the points
- logarithm
- a power to which a base, [actually 10] must be raised to produce a given number

If n^{x}= a, the logarithm of a, with n as the base, is x. - logarithmic function
- function written in the simple base form
*y*= log_{B}(*x*)

These functions can be rewritten without logarithms in the equivalent statement:*x = B*Only positive real numbers have real logarithms. You cannot take the logarithm of a negative number. For instance,^{y}*y*= log_{2}(*-*4) is undefined since the equivalent statement: -4 = 2^{y}has no solution. You cannot raise 2 to any power (*y*) to generate -4 as the answer. - major axis
- the line that runs through the foci, center, and vertices of a hyperbola
- mapping diagram
- a diagram that illustrates how each element of the domain of a relation is paired with a corresponding element of the range of the relation
- matrix
- a rectangular arrangement of numbers

"Matrices" is the plural form of "matrix". - maximum value
- the highest point on the graph of the quadratic function
- minimum value
- the lowest point on the graph of the quadratic function
- minor axis
- the line through the center of a hyperbola that is perpendicular to the major axis
- multiplying binomials
- Use the FOIL method to multiply binomials.
- no solution
- when there isn’t any value that will make the equation true
- one-to-one function
- a function where every element of the range corresponds to exactly one element of the domain and passes both the vertical line test and the horizontal line test
- parabola
- a U-shaped curve that is the graph of a quadratic function
- parameter
- a constant in a function or equation that may be changed
- parent function
- the simplest function for a family of functions
- perfect square trinomial
- a trinomial that is the square of a binomial

Perfect squares factor into either the square of a sum such as (*x*+ 3)^{2,}or the square of a difference such as (*x*- 9)^{2}. - piecewise
- a function that is a combination of pieces of two or more other functions
- polynomial
- an expression with one or more terms containing variables, real numbers, or products of one or more variables and a real number with whole-number exponents
- polynomial form
- an equation that is written as a polynomial;
*y = ax*is the polynomial form of a quadratic equation^{2}+ bx + c - principal square root
- the unique nonnegative square root of a nonnegative real number
- quadratic
- a second degree equation, which can be written in general form
*y = Ax*^{2}+*Bx + C* - quadratic expression/quadratic function
- a polynomial function whose highest exponent is 2; the graph is a parabola

The general form is: f(x) = ax^{2}+ bx + c. - quadratic formula
- the formula which gives solutions or roots for equations of the
form
*ax*^{2}+*bx*+*c*(*a*≠ 0) - radical
- a root of a quantity, e

Example: √*x* - radicand
- the number or expression under a radical sign
- radius
- a line segment between the center and a point on the circle
- range
- the set of values of the dependent variable for which a function is defined
- rational function
- the quotient of two polynomials where the denominator has a degree greater than zero

In other words, there needs to be a variable in the denominator to be a rational function - rational number
- any number that can be expressed as a ratio (fraction)
- real number
- every point on the number line; can be either a rational or irrational number
- Reduced Row Echelon Form (RREF)
- a matrix form in which each row is reduced to a 1 along the diagonal

All entries above and below the diagonal are 0’s. - reflection
- a transformation "flips" across a line (called the line of reflection)

Only the location of the graph changes, the shape stays the same. - relation
- a set of ordered pairs
- restricted domain
- the domain of a function is restricted when there are values of
*x*that cannot be used, when you substitute in an*x -*value the*y*-value is undefined or imaginary - roots
- the solution(s) of a quadratic equation
- square
- to raise a number or expression to the 2nd power
- square root function
- a function whose rule contains a variable beneath a square-root sign
- simulate
- an activity that represents a real-world situation without the need to actually perform the real-world situation
- solution
- roots, zeros,
*x*-intercepts, or values where the function equals zero - solution to a system of equations
- the point or points of intersection for all equations in the system
- standard form
- a quadratic equation written in the form:
*y*=*ax*^{2}+*bx*+*c*, where a ≠ 0 - stretch
- a transformation that pulls the points of a graph vertically away from the x-axis
- substitution
- the act of replacing a variable with a number or expression equal in value
- symmetric
- if a graph is symmetric, two parts of the graph are congruent to each other
- system of inequalities
- two or more inequalities containing common variables
- system of linear equations
- two or more equations involving the same variables and worked upon together
- transformation
- a change in the shape or location of a graph
- translation
- a change in only the location of a graph; all of the points in the graph move the same distance in the same direction and the shape of the graph stays the same
- transverse axis
- the line through the center of the hyperbola that includes the foci
- trinomial
- a polynomial with three terms
- variable
- usually) letters or other symbols representing unknown numbers or values
- vertex
- for a quadratic function, the lowest (minimum) or the highest (maximum) point on the graph
- vertex form
*y*=*a*(*x*–*h*)^{2}+*k*, where a, h, and k are constants and (h,k) is the vertex of the parabola- vertical asymptote
- a line that a graph approaches more and more closely
- vertical shift
- movement of a graph up or down

A function*f(x)*can be moved “*k*” units up/down by performing the operation*f*(*x*) ±*k*. *x*-intercept- the point(s) where the function crosses the
*x*- axis *y*-intercept- the point(s) where the function crosses the
*y*- axis - Zero Product Property
- If
*ab*= 0, then*a*= 0 or*b*= 0

*Example:*If (*x*+ 1)(*x*+ 2) = 0, then (*x*+ 1) = 0 or (*x*+ 2) = 0. - zeros
- the solution(s) of a quadratic equation; a value of x that makes a function
*f*(*x*) equal to 0, a zero of a function may be real or imaginary