Algebra 2 Chapter 1 Vocabulary. identity  A statement that equates two equivalent expressions.


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1 Chapter 1 Vocabulary identity  A statement that equates two equivalent expressions. verbal model A word equation that represents a reallife problem. algebraic expression  An expression with variables. exponent  The number in a power that represents the number of times the base is used as a factor. equation  A statement in which two expressions are equal. terms  The parts of an algebraic expression that are added together. numerical expression  An expression that consists of numbers, operations, and grouping symbols. variable  A letter that is used to represent one or more numbers. value  The result when the variables in an algebraic expression are replaced by numbers and the expression is simplified. coordinate  The number that corresponds to a point on a number line. rational numbers  Numbers that can be written as the ratio of two integers. integers  The numbers..., 3, 2, 1, 0, 1, 2, 3,... graph of a real number  The point on a number line that corresponds to a number. order of operations  Set of rules that gives the order in which operations should be performed when evaluating expressions. power  An expression such as 2 5, which represents = 32.
2 Chapter 2 Vocabulary independent variable  The input variable in an equation. range  The set of output values for the relation. relation  A mapping, or pairing, of input values with output values. step function  A piecewise function whose graph resembles a set of stair steps. linear function  A function of the form y = mx + b where m and b are constants. Its graph is a line. piecewise function  A function represented by a combination of equations, each corresponding to a part of the domain. function  A relation with exactly one output for each input. "x" intercept  The xcoordinate of the point where a line intersects the xaxis. parallel lines  Two lines in a plane that do not intersect. dependent variable  The output variable in an equation, which depends on the value of the input variable. domain  The set of input values for the relation. slope  The ratio of vertical change (the rise) to horizontal change (the run) for a nonvertical line.
3 Chapter 3 Vocabulary "y" intercept  If the graph of an equation intersects the yaxis at the point (0, b), then the number b. Given the equation of the graph, it is the value of y when x = 0. " z" axis  The vertical line through the origin and perpendicular to the xycoordinate plane in a threedimensional coordinate system. three dimensional coordinate system  Is a coordinate system determined by three mutually perpendicular axes. octants  When taken pairwise, the axes of a threedimensional coordinate system form three coordinate planes that divide space into eight parts objective function  In linear programming, the linear function that is optimized. Linear combination  A method for solving linear systems. Step 1: Multiply one or both of the equations by a constant to obtain coefficients that differ only in sign for one of the variables. Step 2: Add the revised equations from Step 1. Combining like terms will eliminate one of the variables. Solve for the remaining variable. Step 3: Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable. constraints  In linear programming, the linear inequalities that form a system. optimization  A process in which you find the maximum or minimum value of some variable quantity. system two of linear equations  Two equations of the form Ax + By = C and Dx + Ey = F where x and y are variables, A and B are not both zero, and D and E are not both zero. feasible region  In linear programming, the graph of the system of constraints. "x" intercept  The xcoordinate of the point where a line intersects the xaxis. Given an equation of the line, it is the value of x when y = 0. solution  An ordered pair (x, y) that makes the equation a true statement when the values of x and y are substituted in the equation. slope  The ratio of vertical change (the rise) to horizontal change (the run) for a nonvertical line.
4 Chapter 4 Vocabulary column matrix  A matrix with only 1 column. Cramer's rule  A method for solving a system of linear equations which uses determinants of matrices. solution  An ordered pair (x, 0) that satisfies each equation of the system. equal matrices  Matrices that have the same dimensions and equal entries in corresponding positions. matrix  A rectangular arrangement of numbers in rows and columns. dimensions  The number m of rows of a matrix by the number n of columns of a matrix, written m x n. constant term  A term that has no variable part. entries  The numbers in a matrix. zero matrix  A matrix whose entries are all zeros. row matrix  A matrix with only 1 row. square matrix  A matrix with the same number of rows and columns. scalar  A real number by which you multiply a matrix.
5 Chapter 5 Vocabulary vertex  The point of a parabola that lies on the axis of symmetry. radicand  The number or expression beneath a radical sign. trinomial  An expression with three terms. factoring  A process used to write a polynomial as a product of other polynomials having equal or lesser degree. parabola  The set of all points equidistant from a point called the focus and a line called the directrix. complex conjugates  Two complex numbers of the form a + bi and a  bi. Their product is always a real number. vertex form  The form y = a(x  h) 2 + k where the vertex of the graph us (h, k) and the axis of symmetry is x = h. complex number  A number a + bi where a and b are real numbers and i is the imaginary unit. rationalizing  The process of eliminating a radical in the denominator of a fraction by multiplying both the numerator and the denominator by an appropriate radical. monomial  An expression with one term. binomial  An expression with two terms.
6 Chapter 6 Vocabulary fundamental theorem of algebra  If f(x) is a polynomial of degree n where n > 0, then the equation f(x) = 0 has at least one root in the set of complex numbers. repeated solution  For the equation f(x) = 0, if and only if the factor (x  k) has degree greater than 1 when f is factored completely. end behavior  The behavior of the graph of a function as x approaches positive infinity or negative infinity. standard form  The form of a polynomial function where the terms are written in descending order of exponents from left to right. polynomial long division  A method used to divide polynomials similar to the way you divide numbers. factoring by grouping  A method used to factor some polynomials with pairs of terms that have a common monomial factor. synthetic division  is a method used to divide a polynomial by an expression of the form x  k. quadratic form  The form au 2 + bu + c where u is any expression in x. "x" intercept  The xcoordinate of the point where a line intersects the xaxis. Given an equation of the line, it is the value of x when y = 0. remainder theorem  If a polynomial f(x) is divided by x  k, then the remainder is r = f(k). power  An expression such as 2 5, which represents = 32. factor theorem  A polynomial f(x) has a factor x  k if and only if f(k) = 0.
7 Chapter 7 Vocabulary relation  A mapping, or pairing, of input values with output values. median  The middle number when n numbers are written in order. (If n is even, it is the mean of the two middle numbers.) statistics  Numerical values used to summarize and compare sets of data. inverse functions  A relation and its inverse relation whenever both relations are functions. range  The difference between the greatest and least data values. mode  The number or numbers that occur most frequently in a set of n numbers. mean  The sum of n numbers divided by n. Also called average. exponent  The number in a power that represents the number of times the base is used as a factor. measures of dispersion  Used statistics that tell you how spread out the data are. They include the range and the standard deviation. like radicals  Two radical expressions that have the same index and the same radicand. frequency distribution  A table that shows the frequencies for the intervals into which data are grouped. square root  What r is in r 2 = s. standard deviation  is the typical difference between the mean and a data value.
8 Chapter 8 Vocabulary relation  A mapping, or pairing, of input values with output values. base  What b is in a function involving the expression b x where b is a positive number other than 1. natural logarithm  The logarithm with base e. exponential function  involves the expression b x where the base b is a positive number other than 1. exponential decay function  is a function of the form f(x) = ab x where a > 0 and 0 < b < 1 (decrease). exponent  The number in a power that represents the number of times the base is used as a factor. growth factor  The quantity 1 + r in the exponential growth model y = a(1 + r) t where a is the initial amount and r is the percent increase expressed as a decimal. base of power  The number in a power that is used as a factor. inverse function  A relation and its inverse relation whenever both relations are functions. decay factor  The quantity 1  r in the exponential decay model y = a(1  r) t where a is the initial amount and r is the percent decrease expressed as a decimal. function  A relation with exactly one output for each input. power  An expression such as 2 5, which represents = 32. asymptote  A line that a graph approaches as you move away from the origin.
9 Chapter 9 Vocabulary joint variation  A relationship that occurs when a quantity varies directly as the product of two or more other quantities verbal model  A word equation that represents a reallife problem. "y" intercept  If the graph of an equation intersects the yaxis at the point (0, b). Given the equation of the graph, it is the value of y when x = 0. complex fraction  A fraction that contains a fraction in its numerator or denominator. asymptote  A line that a graph approaches as you move away from the origin. hyperbola  The set of all points P such that the difference of the distances from P to two fixed points, called the foci, is constant. branches  The two symmetrical parts of a hyperbola. relation  A mapping, or pairing, of input values with output values. "x" intercept  The xcoordinate of the point where a line intersects the xaxis. Given an equation of the line, it is the value of x when y = 0. direct variation  y = kx where k is a nonzero constant. cross multiplying  A method of solving a simple rational equation for which each side of the equation is a single rational expression. Equal products are formed by multiplying the numerator of each expression by the denominator of the other.
10 Chapter 10 Vocabulary transverse axis  The line segment joining the vertices of the hyperbola. circle  The set of all points (x, y) that are equidistant from a fixed point, called the center. hyperbola  The set of all points P such that the difference of the distances from P to two fixed points, called the foci, is constant. vertex  This point is the lowest or highest point on a parabola with a vertical axis of symmetry and the leftmost or rightmost point on a parabola with a horizontal axis of symmetry. radius  The distance r between the center of the circle and any point (x, y) on the circle. directrix  Perpendicular to the axis of symmetry. parabola  The set of all points equidistant from a point called the focus and a line called the directrix. minor axis  The line segment joining the two covertices of an ellipse. ellipse  The set of all points P such that the sum of the distances between P and two distinct fixed points, called foci, is a constant. conic section  A curve formed by the intersection of a plane and a doublenapped cone. covertices  The points of intersection of an ellipse and the line perpendicular to the major axis at the center. focus  Lies on the axis of symmetry of a parabola.
11 Chapter 11 Vocabulary terms  For a sequence of numbers, the numbers in the sequence. geometric series  The expression formed by adding the terms of a geometric sequence. arithmetic sequence  A sequence in which the difference between consecutive terms is constant. rational numbers  Numbers that can be written as the ratio of two integers. factorial  The expression n! and represents the product of all integers from 1 to n. range  The set of output values for the relation. domain  The set of input values for the relation. integers  The numbers..., 3, 2, 1, 0, 1, 2, 3,... geometric sequence A sequence in which the ratio of any term to the previous term is constant. function  A relation with exactly one output for each input. finite sequence  A sequence that has a last term. sequence  A function whose domain is a set of consecutive integers. common difference  The constant difference between consecutive terms of an arithmetic sequence. finite differences  To decide whether yvalues for equallyspaced xvalues can be modeled by a polynomial function. series  The expression that results when the terms of a sequence are added.
12 Chapter 12 Vocabulary factorial  The expression n! and represents the product of all integers from 1 to n. symmetric distribution  A distribution in which the left half of the histogram representing the distribution is a mirror image of the right half. dependent events  Two events such that the occurrence of one affects the occurrence of the other. independent events  Two events such that the occurrence of one has no effect on the occurrence of the other. experimental probability  A calculation of the probability of an event based on performing an experiment, conducting a survey, or looking at the history of an event. probability  A number between 0 and 1 that indicates the likelihood an event will occur. compound event  The union or intersection of two events. combination  A selection of r objects from a group of n objects where the order is not important. standard deviation  The typical difference between the mean and a data value. permutation  An ordering of objects. fair game  A game for which the expected value is 0. geometric probability  A type of probability found by calculating a ratio of two lengths, areas, or volumes. mean  The sum of n numbers divided by n. Also called average.
13 Chapter 13 Vocabulary circle  The set of all points (x, y) that are equidistant from a fixed point, called the center. parameter  A variable, usually denoted t, upon which two other variables depend. parametric equations  Are equations that express two variables in terms of a third variable, called the parameter. radius  The distance r between the center of the circle and any point (x, y) on the circle. sector  A region of a circle that is bounded by two radii and an arc of the circle. coterminal angles  Two angles in standard position with terminal sides that coincide. terminal side  The rotating ray of an angle. central angle  An angle formed by two radii of a circle. angle of depression  The angle from a horizontal line through an object A to a line connecting object A and a lower object B. radian measure  In a circle with radius r and center at the origin, The measure of an angle in standard position whose terminal side intercepts an arc of length r. domain  The set of input values for the relation.
14 Chapter 14 Vocabulary local minimum  The ycoordinate of a turning point of the graph of a function if the point is lower than all nearby points. frequency  The reciprocal of the period. domain  The set of input values for the relation. relation  A mapping, or pairing, of input values with output values. identity  A statement that equates two equivalent expressions. period  The horizontal length of each cycle of a periodic function. "y" intercept  If the graph of an equation intersects the yaxis at the point (0, b). Given the equation of the graph, it is the value of y when x = 0. local maximum  The ycoordinate of a turning point of the graph of a function if the point is higher than all nearby points. quadratic form  The form au 2 + bu + c where u is any expression in x. range  The set of output values for the relation. function  A relation with exactly one output for each input. "x" intercept  The xcoordinate of the point where a line intersects the xaxis. Given an equation of the line, it is the value of x when y = 0. asymptote  A line that a graph approaches as you move away from the origin. cycle  The shortest repeating portion of a periodic function.
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