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Word Definition Examples The x-value of an ordered pair that describes the vertical distance from the x-axis. Abscissa It is always written as the first element in the ordered pair. 3 is the abscissa of the ordered pair (3, 5). Absolute Value Distance of a number from zero on a number line. Since distance is always positive, the absolute value of any number must be positive. Caution: be careful when taking the absolute value of a variable, since you may have several possible correct solutions. Additive Identity 0 - zero 0 is the additive identity in algebra because When you add zero to anything it does a+0=0+a=a not change the value. Additive Inverse A number and its opposite Algebra The study of equations using variables. At Huguenot High School, the study of algebra is broken into Algebra 1 and Algebra 2. Algebraic expression A collection of letters (variables) and real numbers (constants) combined using the operations of addition, subtraction, multiplication, division, and exponentiation. Algorithm In mathematics, an algorithm is often a step-by-step procedure. Arithmetic Mean The arithmetic mean of numbers is the sum of the numbers divided by how The mean of 3 and 8 is 5.5 many numbers you added - also called the average Argument Numeric or algebraic input into an algorithm, n function, or other defined function Arithmetic Sequence A numerical pattern where the The arithmetic sequence 1, 4, 7, 10, 13, ... difference between consecutive terms has a common difference of 3 is a constant Arithmetic Series Associative Property When you add them they equal zero. |5|=5 |- 5| = 5 5 and -5 are inverses because 5 + (-5) = 0 th The sum of the terms of an arithmetic sequence Changing the grouping of addends or factors does not change the sum or product. Grouping doesn't matter when (2 + 3) + 4 = 5 + 4 = 9 2 + (3 + 4) = 2 + 7 = 9 (2 x 6) x 5 = 12 x 5 = 60 adding or multiplying 2 x (6 x 5) = 2 x 30 = 60 Asymptote A line the graph of a function gets close to but does not cross Axis of Symmetry The line about which you can reflect a graph onto itself also the vertical line containing the vertex of a parabola When you fold a graph For the parabola, on the axis of y = x2 + 4x - 5 the axis of symmetry is the symmetry, both sides line x = 2 match Back-to-Back Stem and Leaf A stem-and leaf plot used to compare two related sets of data Plot Bar Graph A graph where data is shown in bars that are used to compare amounts. The length of each bar represents the frequency Base In an expression of the form xn, x is the base and n is the exponent. Best Fit Line The straight line that most closely approximates the data in a scatter plot. Binary operation An action performed on two quantities Addition, subtraction, multiplication, division and exponentiation are binary operations. Binomial Polynomial expression with two terms - bi means two 2x + 3 Binomial Experiment An experiment that has only two possible outcomes Tossing one coin is binomial because you only get heads or tails Binomial Theorem The expansion of (a + b)n where n is a positive integer is: (x + 3)2= x2 + 6x + 9 is a binomial (a + b)n= C0an + C1an-1b1 + C2an-2b2 + ... + Cn-1a1bn- expansion 1 + Cnbn Bounded intervals Intervals with defined end points on the real number line used to define the domain of an inequality. See unbounded intervals Box and Whisker Plot A diagram that divides a set of data into four parts: lower quartile, below the mean (average), above the mean, and highest quartile. /td> Branch Each piece of a discontinuous graph. [a,b] means a ≤ x ≤ b, a closed interval (a,b) means a < x < b, an open interval [a,b) means a ≤ x < b (a,b] means a < x ≤ b y = (x + 5)/(x-5) has two branches and is discontinuous at x = 5 Central tendency The tendency of data to be grouped near the Measured using mean, median, and center of the data. mode. Certain Event An event whose probability is one (1) or 100% Something that always happens Closed interval An interval that includes both of its end points. Closure Property A set is said to be closed under some operation if the operation on members of the set produces a member of the set. A set that is closed under an operation or collection of operations is said to satisfy a closure property. For example, the real numbers are closed under subtraction, where the subset of natural numbers is not. Combination An arrangement or listing where the order is not important. Picking three students out of a classroom Coefficient The numerical factor when a term has a variable 5y 5 is the coefficient and y is the variable Common Factors Numbers, variables, and any products formed For 2x2 -6x from the prime factors that appear in all 2 and x are the common factors terms of an expression Common logarithm A base 10 logarithm Commutative Property Changing the order of addends or factors does not change the sum or product Completing the Square One method used to solve a quadratic equation. Other methods include factoring and the quadratic formula. Complex fraction A fraction where the numerator, denominator, or both has a fraction Complex Number A number of the form a + bi, where a and b are Also called an imaginary number real numbers and i is the square root of -1. The number next to a letter Order doesn't matter when adding or multiplying 2+3=3+2=5 5 x 4 = 4 x 5 = 20 5 ¾ Combining two functions by taking the output of one and Composition of using it as the input of another functions If the output of g is used as the input of f, then the composition is referred to as "f of g of x" and is denoted f(g(x)) or f ○ g(x) Consistent system (of equations) A system of equations that has at least one solution 5 -3.7 Constant A value or number that never changes Constant of variation The non-zero (usually denoted k) in a direct variation (y=kx), an indirect variation (y= kx ) or a joint variation (z=kxy) Constant Term A term that has no A number that stands alone variable factor Continuous Data Measures that change Things that could be measured at temperature, height, time, blood between any time - they always exist pressure, average grade data points Continuous Function Function whose graph is an unbroken curve - it does not have any holes, gaps, or jumps 7x + 3 3 is the constant term Coordinate of On a number line, it is the distance of the point from the origin. On a coordinate a point axis is the pair (x, y) that defines the location. Coordinate Plane Formed when two number lines intersect at right angles. The x-axis is the horizontal axis and the y-axis is the vertical axis. The two axes meet at the origin (0,0). Correlation A trend between two sets of data. A trend may show positive correlation (both sets of data get bigger together) negative correlation (one set of data gets bigger while the other gets smaller), or no correlation. An equation in the form Largest 3 2 Cubic Equation ax + bx + cx + d = y, where a, b, c, exponent is and d are real numbers and a ≠ 0 3 2x3 + 3x2 -5x + 7 = y Data Numbers collected for use in statistics and other forms of problem solving. Decimals A number written with place value instead of fractions or mixed numbers. Also used to approximate irrational numbers. See repeating decimals, truncated decimals , and non-repeating decimals. Decreasing function A function f is decreasing on an interval if and only if for every a and b in the interval, f(a) > f(b) whenever a < b. Degree of a monomial The sum of the exponents of all its variables Degree of a For a polynomial with only one The biggest 2.25 = 2 ¼ decimal fraction 7x5y2 is 5 + 2 or 7th degree 7x5 + 3x2 - 8= y is fifth degree polynomial (single variable) variable, the highest degree of any of its terms positive exponent Degree of a polynomial (multiple variables) For a polynomial with more than one variable, the highest degree of any of its terms 7x5y2 + 3x2y2 - 8 is 7th degree because the first term is degree 7, the second term is degree 4, and the number term is degree zero. Dependent events In probability, when the outcome of one event affects the outcome of a second event, the events are dependent The probability of getting 2 heads in a row when you flip coins depends on if you get a head the first toss. Dependent system of equations system of linear equations where one linear equation is a multiple of the other and, therefore, has an infinite number of solutions Dependent variable A variable that relies on the value of another variable A quadratic binomial of the Difference of form a2 - b2, it two squares factors to (a + b)(a - b) Direct variation Discrete Data for y = x + 2, the value of y depends on the value of x Perfect square minus a perfect x2 - 9 square 4x2 - 25 A linear function A straight line that passes of the form y = kx, through (0,0) with slope k where k ≠ 0 y = 5x y = -2x Involves a count of Things that can be counted data items heart beats in a minute daily temperature at noon Discontinuous A graph of a function that has jumps, holes or breaks. It cannot be graphed without Function lifting your pencil. the term under the square root sign in the quadratic formula: b2 - 4ac Discriminant Distributive property if the discriminant is positive the equation has 2 real solutions if the discriminant = zero there is 1 real solution if the discriminant is negative there are 2 imaginary solutions For all real numbers a, b, and c: Multiply everything inside the parenthesis by the 5(x + 2) = 5x + 10 4(x - 2) = 4x - 8 a(b + c) = ab + ac a(b - c) = ab - ac Divisible Domain Element thing in front of the parentheses a number that can be divided by a whole number with no remainder The set of all possible input values - the independent variable in a function. For functions in x and y, the possible x values are the domain. For y = 2x + 6, the domain is all real numbers For y = 7/x, the domain is all real numbers except 0 because you can't divide by zero 1. Each object or number in a set 2. Each entry in a matrix Elimination Using addition or subtraction to eliminate one variable when solving a system of equations. Ellipse For two given points (the foci), an ellipse is the locus of points such that the sum of the distances to each focus is constant. End behavior The way a graph of an equation behaves at the far left and right ends as the input variable goes to positive or negative infinity + ∞ Two expressions Uses the = sign to show the relationship that are that two things are equal to each other. equal. Each side of the equation is an expression. x+2=7 Even function A function graph whose axis of symmetry is the y-axis. y = 5x2 + 2 Even number Any number that can be divided by 2 with no remainder. In Algebra, 2n can represent any even number. Event In probability, any group of outcomes Exact number Any number that is the result of counting or the results from a theoretical calculation. Experimental data In statistics, data that collected from an experiment set up specifically to answer a question. Equation The possible results 4x2 + 2x = 7 When rolling one dice, the outcomes are 1, 2, 3, 4, 5, or 6 Measurements are not exact numbers. Experimental probability In probability, the ratio of the number of times an event happens to the number of times the experiment is done Exponent A raised number that represents repeated multiplication 4 3 =3•3•3•3 of a factor Results from doing an experiment P(event) = times it happened ÷ times you tried y = C(1 - r)t where y is the final amount, C is the original amount, r is the rate of change, and t is time. Exponential decay An equation used to calculate how things get smaller over time - used for radioactive decay and age dating. Exponential function An equation of the form y = bx where there is a variable as an exponent. Exponential functions are the inverse of logarithms Exponential growth An equation used to calculate how things increase over time - used for growth of bacteria and other populations. y = C(1 + r)t where y is the final amount, C is the original amount, r is the rate of change, and t is time. Expression Any combination of values and operations (no = sign) 4x2 + 2x Extraneous Solution A number that comes when you solve an equation, but it doesn't work in the original equation. Frequently occurs in equations with variable under a square root sign. Factoring Breaking a polynomial equation down into the product of several factors y = x2 - 3x + 2 y = (x - 2)(x - 1) Factorial ! n! is the product of all the whole numbers from n down to 1 - used in probability 3! = 3• 2 • 1 = 6 4! = 4 • 3• 2 • 1 = 24 Factors Whole numbers that are multiplied together to equal another number. 2 and 5 are the factors of 10 because 10 = 2 •5 Factored Form A polynomial written as the product of polynomials of lower degree y = (x + 4)(x - 3) is the factored form of y= x2 + x - 12 Favorable outcome In a probability experiment, the possible results you want to happen When flipping coins and you call heads, a favorable outcome is you getting heads. FOIL method F - first terms in each parentheses When multiplying two binomials, use O - outside terms in each parentheses the Distributive property repeatedly. I - inside terms in each parentheses L - last terms in each parentheses Original problem Factored form Fraction A ratio of two numbers representing part of a whole. A fraction is a real number. In Algebra, a fraction bar means to divide. ½ means one half it also means 1 divided by 2 Frequency The number of cycles per unit of time or the reciprocal of the period of the function. Function A relation that assigns exactly one value of the dependent variable to each value of the independent variable Rule that matches y = x + 5 is a function one input to only one if you pick x = 3 you get one answer, y = 8 answer Function notation A function written using the symbol f(x) in place of y Another name for a function - a more f(x) = 2x + 3 formal name. Read it y = 2x + 3 as "f of x" Fundamental Theorem of Algebra Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers. Corollary: Every polynomial P(x) of degree n (n > 0) can be written as the product of a constant k (k ≠ 0) and n linear factors P(x) = k (x – r ) (x – r ) (x – r )…(x – r ) 1 2 3 n Thus a polynomial equation of degree n has exactly n complex roots, namely r , r , r ,…, r . 1 2 3 n Fundamental Theorem of Arithmetic In number theory, the Fundamental Theorem of Arithmetic (or unique factorization theorem) states that every natural number greater than 1 can be written as a unique product of prime numbers. Future value In investment problems with interest, the future value is the value of the investment after interest has been earned. Geometric Sequence A series of numbers where each consecutive number is the prior number times a constant called the common ration. Geometric series The sum of the terms of a geometric sequence. The sum of the first n terms of a ¼, ½, 1, 2, 4, 8, ... has a common ratio of 2 - each number is 2 times the one before geometric series is given by Graph of an equation The set of all ordered pairs (points) that solve the equation. Greatest common factor GCF The largest number that is a factor of two or more whole 7 is the GCF of 14 and 21 numbers. Half-plane One half of a plane On a plane that is divided by a line, each side of the line is a half-plane Hemisphere One half of a sphere On the globe, the northern hemisphere is the top half of the world. Histogram A bar graph that shows the frequency of data in intervals of equal size. The height of each bar shows the number of items in each interval Hyperbola A set of points that are equidistant from a foci. The graph looks a lot like two parabolas on their side. Identity An equation that is true for every value of the variable Always true x+1=1+x Identity Property of Addition The sum of any number and zero is that number Anything + 0 = Itself a+0=a Identity The product of any number Property of and one is that number Multiplication Anything x 1 = Itself a•1=a Imaginary Number A number of the form a + bi, where i is the square root of -1 and i2 = -1 Impossible Event In probability, an event that never happens Improper fraction A fraction where the numerator is larger than the denominator. In arithmetic, you are trained to change these to a mixed number. In Algebra, you should leave it alone. Inconsistent system of equations System of linear equations that has no solutions; parallel lines Increasing A function f is increasing on an interval if and only if f(a) > f(b) for every a > b in the √(-4) = 2i Getting 4¼ when you roll one dice is impossible 7 4 = 1¾ improper mixed function interval. Independent In probability, when the outcome of one event does not affect the outcome of a Events second event, the events are independent Independent system of A consistent system of linear equations with only one solution equations Independent A variable that does not Variable depend on another variable For y = x + 3 x is independent The input variable Index number indicating what root is being taken the index is 4. Inequality One expression that is not equal to another Infinity The concept of something that never ends - infinity is not a number Integer The whole numbers and their opposites Interval A portion of the real number line that may or may not include the end points. The ends of the interval are called the boundaries. Interval notation A short way to define an interval. Brackets [ are used if the end point is part of the interval. Parentheses ( means the end point is not included in the interval. Inverse Operation Operations that undo each other - they are opposite operations addition and subtraction are inverses multiplication and division are inverses squares and square roots are inverses Inverse Variation A function that can be written in the form xy = k or y = k/x As one variable gets bigger, the other gets smaller Irrational number A number that cannot be written as a fraction. A decimal that does not truncate (end) or repeat. Joint variation A relationship that exists when a quantity varies directly with the product of two or more quantities y = kxy Like terms Terms with exactly the same variable factors Line graph A graph that has data points connected by lines Line of best The trend line that most closely matches your data points on a scatter plot. x > 7 means x is greater than 7 -2 < x means negative 2 is less than x 4 < x means x is 4 or bigger ∞ ... - 3, -2, -1, 0, 1, 2, 3, ... [3, 5) means 3<x 5 π = 3.14159... √7 = 2.6457... 6y and -3y are like terms 2ab and 5ab are like terms fit Linear Something that graphs as a straight line, may be an equation or a term within an equation. y = 3x - 2 is a line Linear equation An equation with one variable- no exponents 7 = 2x - 3 Linear The use of a linear equation to predict values that fall outside the range of data. extrapolation Linear function A function that graphs as a straight line. Its form is usually y = mx + b where m is the slope and b is the y-intercept. An alternate form is Ax + By = C y = 2x - 3 or 2x - y = 3 Literal equations An equation that contains more than one variable; an implicit equation; often mathematical formulae Logarithm (log) An exponent: logb x is the power to which the base b must be raised to obtain x Logarithmic function A function in the form y = logb x This is the inverse of an exponential function Matrix A rectangular arrangement of numbers, it uses big brackets to define the matrix. The size of a matrix is # of rows by the # of columns. Maximum value - max The largest value a function can reach. Measures of central tendency Numbers that represent the whole set of data - usually the mean, median, and mode for y = - x2 + 2 the maximum value is 2 for 1, 3, 4, 6 and 6 Mean The sum of a set of numbers divided by the number of items - the average the mean is: (1 + 3+ 4 + 6 + 6)/5 = 4 the median is the middle = 4 Median statistics The middle value in an ordered set - line up the numbers from smallest to largest and find the middle Minimum value The smallest value a function can reach. Mode The data item that occurs most frequently in a set of numbers. A set may have more for y = x2 + 5 the minimum value is 5 for 1, 3, 4, 6 and 6 the mode is 6 than one mode. Mixed number A number written with a whole number part and a fractional part. Monomial a monomial is a product of constants and variables; a polynomial with one term The number that multiples Multiplicative anything without changing identity its value. 2¼ 1 ax1=1xa=a The reciprocal Two numbers that or inverse of a Multiplicative multiply to equal one. Also fraction is the ½ and 2 are inverses because ½ • 2 = 1 inverse called the reciprocal. fraction turned upside down If there are m ways to make a first Multiplication selection and n ways to make a second counting selection, then there are m x n ways to principle make the two selections If there are 3 kinds of crust and 6 kinds of topping, then there are 3 x 6 = 18 different pizza choices Natural logarithm Logarithm to the base e. The function y = ln x is the natural log. It is the same as y = loge x Natural number The counting numbers - the first numbers learned by very small children 1, 2, 3, 4, 5, ... Negative exponent An exponent that is used instead of the reciprocal a-3 = 1/a3 Negative square root -√ - √25 = - 5 is the negative square root of 25 Nonrepeating decimal An irrational number approximated by a decimal. The exact value, if expressed as a decimal would never repeat and never end. √ 2 is approximately 1.414 Normal distribution A statistical frequency distribution that graphs in the shape of a bell curve Observationa In statistics, data that is from seeing something happen or asking someone (doing a l data survey) about what happened. A function graph whose axis of Odd Function symmetry is both the x-axis and the yaxis. It must pass through the origin. Odd number y = 5x3 Any number that has a remainder when divided by 2 . In Algebra, 2n + 1 can represent any odd number. One-to-one function A function where the range elements (the y's) are used only once. y = 2x + 3 is one-to-one Open interval An interval that does not include the endpoints (-4, 5) is the interval between -4 and 5 Operation An action performed on one or two numbers to produce a resulting number. Operations are addition, subtraction, multiplication, division, square roots, and so on. Opposites Additive inverses - they are the same Two numbers that add to distance from zero zero on the number line Order of operations +, -, x, /, ÷, √ + 7 and - 7 are opposites 1. do any operation inside grouping symbols, like parentheses, absolute values, square root signs or the numerator or denominator of a complex fraction 2. simplify terms with exponents 3. multiply and divide in order from left to right 4. add and subtract in order from left to right Ordered numbers Numbers that are arranged in order from smallest to largest or from largest to smallest Ordered pair The location of a point on a coordinate axis Origin The place where the x axis and y axis intersect in a coordinate plane Outcomes The possible results of a probability experiment PEMDAS 5 < 7 < 8.5 6 > 2 > -1 (6, -1) is a point 6 units to the right and 1 unit down from the origin (0, 0) If you flip a coin, the possible outcomes are heads or tails Outlier A value in a data set that is much higher or lower than the rest; a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile Parabola The curved shape you get when you graph a quadratic function Percent % A portion of 100 Perfect squares Numbers whose square roots are 1, 4, 9, 16, 25, 36, and 49 are perfect squares rational numbers ¼ is also a perfect square Piecewise function A function that consists of one or more functions, each with a limited or specified domain; when the pieces are graphed, on the same coordinate plane, the graph may or may not be continuous. Polynomial A statement with one or more terms - poly means many 5x2, -72, and 3x2 + 2x - 1 are polynomials Power The exponent x5 is x to the fifth power Prime polynomial a polynomial that cannot be factored over the real numbers further x +4 Probability The chance that something will happen. For example, the probability that you will get a head when you flip one coin is 1 chance out of 2 or 1/2. Properties In geometry, statements that are accepted as true and are used with deductive reasoning to prove other statements. Proportion A statement that two ratios are equal - two fractions that are equal Pure imaginary number A complex number a + bi, where a = 0 and b is not zero Quadrants The coordinate x-y plane is divided into four quadrants by the x axis and y axis. Quad means four. The quadrants are usually labeled with roman numerals, starting at the top right and numbering counterclockwise. Quadratic An equation written .65 = 65/100 = 65% The largest 2 1 5 II = 3 15 I III 2x2 - 3x + 4 = 0 IV equation in the form ax2 + bx + c = 0 where a, b, and c are real numbers and a ≠ 0 exponent is 2 -b ± √(b2 - 4ac) Quadratic formula if ax2 + bx + c = 0 and a ≠ 0, then x = Quadratic function A function with an equation written in the Graph as a parabola - the largest form exponent is 2 y = ax2 + bx + c where a ≠ 0 y = 2x2 - 3x + 4 Radical A square root sign or any other root, like a cube root or fourth root √5 Range (of a function) The set of all possible output values of a function - the dependant variable. For Possible answers functions in x and y, the possible y values are the range. 2a for y = |x| the range is all positive numbers and 0 The range of {5, 7, 9, 2, 4, 7, 1, 7} is 8 because the maximum value is 9 and the minimum value is 1. Range (of a set of data) the difference between the maximum value and the minimum value in a data set Ratio Comparing two numbers by division Rational expression An expression with fractions, especially when there is a variable in the denominator. The variable can not make the denominator equal to zero Rational Function A function that can be written as R(x) = P(x) / Q(x) where P(x) and Q(x) are polynomials and Q(x) ≠ 0. Rational number A number that can be written as a fraction. This includes whole numbers, fractions, and decimals that truncate (end) or repeat. Rationalize the denominator Make the denominator of a fraction a rational number without changing the value of the expression Real number A number that is either rational All numbers except or irrational imaginary numbers A fraction ¾ and 3:4 ½, ¾, 2.5 and -3 are rational 3√5 Get rid of any √ signs 3 = in the denominator √5 5 √5, ½, ¾, 2.5, 0, π and -3 are real numbers 2 3 and 3 2 are reciprocals because 2 3 • =1 3 2 Reciprocal Multiplicative inverse of a nonzero number. The product of a number and its reciprocal is 1. Regression Linear regression is the process of obtaining the line of best fit. The relationship between two sets of data may be described with a line using some goodness-of-fit criterion. The regression line obtained may be used to describe data and make predictions. Relation Any set of ordered pairs Relationship symbols Symbols that compare two numbers. This includes the equal sign. Repeating decimal A decimal expression of a fraction, where the digits repeat. The repeating part is written with a bar over it to represent that the pattern repeats infinitely. Roots (of a polynomial) A root of a polynomial is a number x such that P(x)=0. A polynomial of degree n has n roots. Sample Space In probability, all the possible ways that an event can happen. Scatter plot A graph that relates Scatter plots frequently have dots or x's ordered sets of data. To get the reciprocal; Flip it! 5<7 -2 > -8 1/3 = 0.33333... 3450 = 3.45 x 103 Scientific Notation A number expressed in the form a x 10n where n is an integer and 1 < a < 10. For a number between 0 and 1, the exponent n will be a negative. Sigma Σ σ Greek letter used in math and statistics problems Simple fraction A fraction that has one number in the numerator and one number in the denominator Simple Interest Interest calculated using the formula I = prt, The interest on $300 at 5% per year where I is interest paid, p is principle, r is for 4 years is I = prt = 300(.05)(4) = the interest rate charged, and t is the time $60 period. Simplify Combine all like terms that can be combined 5 + 3 simplifies to 8 and get rid of parentheses to cut down on the 0.052 = 5.2 x 10-2 12 17 number of terms in an expression Slope The measure of the steepness of a line. Slope is the change in y (up and down) divided by Δy slope = m = the change in x (left and right). Δx Slope is abbreviated m. SlopeIntercept form A linear equation written in the form y = mx + b, where m is the slope and b is the yy = 2x + 4 intercept Solve Find the answer. In algebra, it means to figure out what the variable stands for. Solution or root A number that makes an equation a true statement Solution set The set of all numbers that satisfy an equation (make it true). Square Root If a2 = b, then a is the square root of b. Square root is the opposite of square. Standard Form of a Polynomial When the degree of the terms in a polynomial decrease from left 5x3 + 3x2 - x + 8 to right. Statistics The branch of mathematics that deals with the collection, analysis, interpretation, explanation, and presentation of data. Subtraction Adding the opposite 7x - 3x = 7x + (-3x) = 4x System of Linear Equations Two or more linear equations for which a common solution is sought. The solution is where the two lines cross when graphed. Table of Values A method for finding points that solve an equation so the equation can be graphed. You guess an x, then plug y = 3x + 4 it into the equation to solve for the matching y value. Continue until you have enough (x,y) pairs to graph. Term A grouping together of one or more factors (variables and/or number). Multiplication or division connects letters to numbers in a term. x+5=7 so x = 2 x 5 and -5 are square roots of 25 y = 3x + 4 points -2 -2 = 3(-2) + 4 (-2,-2) -1 1 = 3(-1) + 4 (-1, 1) 0 4 = 3(0) + 4 ( 0, 4) 1 ( 1, 7) 7 = 3(1) + 4 2 10 = 3(2) + 4 4xy is one term 3xy + 5x – 6 has three terms ( 2,10) Addition and subtraction symbols separate terms. Theoretical Probability The calculated chance that something will happen based on the number of ways possible in tossing a coin, the theoretical probability of getting heads is: P(heads) = ½ Translation When a graph is shifted in a horizontal or vertical direction. Trend Line A line on a scatter plot that can be drawn to pass through the points. The trend line shows the correlation between the two sets of data. Trinomial A polynomial expression with three terms Truncated decimal A fraction, that when converted to a decimal ends with repeating zeros. Because math people are so lazy, they don't write the zeros or show them as a repeating digit. ¼ = 0.250000..... = 0.25 Two-Step Equation An equation that has two operations and requires two steps to solve. 7x - 5 = 9 is a two-step equation Unbounded intervals Intervals with end points at + ∞ on the real number line used to define the domain of an inequality. See bounded intervals [a,∞) means x ≥ a (a,∞) means x > a, an open interval (-∞,b] means x ≤ b (-∞,b) means x < b, an open interval (-∞,∞) means the entire number line Unknown The value represented by a letter in an equation. The unknown is also called the variable. Variable A letter or symbol that is used to represent a number. When a variable is used in an equation, the equation can be solved to find the value of the variable. This value is the solution to the equation. Variable expression A mathematical phrase that contains at least one variable x a z 8 - x is a variable expression Vertex The point on a parabola where the arch turns. If the parabola opens up, the vertex is the smallest value of the function. <> Vertical line test A method used to determine if the graph of a relation is a function. For all functions, a vertical line will never cross the graph more than once. Whole Number The non-negative integers including zero Work backwards A method that can be used to solve word problems. Read the problem first, then see if it is possible to do the steps starting at the end. x-axis The horizontal axis of the coordinate plane 0, 1, 2, 3, 4, 5, 6, ... See graphing lines The first number in an ordered pair. (5, 3) x-coordinate It indicates the distance left or 5 is the x-coordinate right horizontally from the origin. x-intercept The x-coordinate of the point where The x-intercept of a line crosses the x-axis y = 2x + 4 is -2 y-axis The vertical axis of the coordinate plane See graphing lines y-coordinate The second number in an ordered pair. It indicates the distance up or down vertically from the origin. (5, 3) 3 is the y-coordinate y-intercept The y-coordinate of the point where The y-intercept of a line crosses the y-axis For equations in the form y = ax2 + bx + c, the c coeffcient is always the y-intercept y = 3x + 2 is 2 Zero Matrix A matrix where all the elements are zero. For any two real numbers multiplied Zero Product together so the answer is zero, at least one Property of the numbers multiplied must be zero. Used when factoring to solve an equation. If ab = 0, a or b or both must equal zero Zeros All the places where a graph crosses The x-intercepts of an equation. The points for which f(x) = 0 the x axis.