A Addition of integers, 1 linear equations, 4 linear inequalities, 54 of polynomials, 337, 340 341, 396 Property of Equality, 4 of Inequality, 54 of radicals and square roots, 465, 470 in units of measure, 2 Algebra tiles, 336, 337, 345, 357, 371, 377, 383 Algebraic expressions, simplifying, 335 Analyzing Mathematical Relationships, Throughout. See for example: patterns and structure in arithmetic sequences, 201 compound inequalities, 75 equations with variables on both sides, 21 a multi-step inequality with variables on both sides, 69 and (intersection), 74, 75 Angles measuring, 3 of a polygon, for angle measures of, 11 Another Way arithmetic sequences, 204 equation of horizontal line, 175 equation of line, 174 equations in standard form, possible combinations, 176 graphing quadratic functions, 429 negative exponent, 280 parallel lines, 180 perpendicular lines, 181 set-builder notation, 48 linear systems by graphing, 239 linear systems by inspection, 238 quadratic equations, 477, 486, 488 system of linear equations by elimination, 233 system of linear equations by substitution, 227 transformations, 144 zeros of functions, 478 Area of equilateral triangle, 488 formulas, 27, 29 rewriting formula for surface area, 29 equations with variables on both sides, 21 Arithmetic sequence(s), 201 205, 212 defined, 201, 202 equations for, 204, 275 graphing, 203 nth term of, 275 writing as functions, 204 writing terms of, 202 Asymptote, 293 Average rate of change comparing functions using, 448 449 defined, 448 Axis of symmetry defined, 406 finding vertex and, 418 B Binomial(s) defined, 339 as factors of trinomials, 371, 377 multiplying, 345 348 with a trinomial, 348 using FOIL Method, 347, 353 square of binomial pattern, 351 352 sum and difference pattern, 351, 353 Break-even point, 219 Byte, units of measure, 283 C Causation and correlation, 197 Circle circumference, 27 radius formula, 64 Closed, set of numbers, 340 Coefficient of determination, 480 Common difference, 202 Common Errors axis of symmetry, 419 completing the square, 495 falling objects, 414 negative sign in inequality, 61 polynomial long division, 359 polynomials, 340 recursive rule for sequence, 321 unit of time, 31 Common problem- strategies, 7 Common ratio, 312 Completing the square defined, 494 finding maximum and minimum values, 496 quadratic equations by, 493 495, 508, 516 Compound inequality(ies) defined, 74, 73 76, 82 Compound interest, 303 Concept Summaries factoring polynomials completely, 391 factoring a trinomial, relationships between signs, 374 number of solutions of quadratic equation, 477 representation of functions, 99 representing linear inequalities, 49 slope, 125 linear equations, 23 systems of linear equations, 233 Cone radius, 290 volume, 27 Conjecture, 3, 123 Conjugates defined, rationalizing the denominator with, 468 of golden ratio, 474 Consistent dependent system, 239, See also Infinitely many solutions Constant function, 126 Constant of variation, 134 Continuous data, graphing, 101 Continuous domain, 100 Coordinate plane, 159 Correlation between data sets, 189 defined, and causation, 197 Correlation coefficient, 195 Counterexample, 465 Cube roots finding, 285 using properties of, 467 Cubic function(s), 438, 440 Cylinder, volume of, 281, 394 A53
D Data correlations between, 189 interpolating and extrapolating, 197 modeling with lines of fit, 190 writing functions to model, 448, 450 Decay, See Exponential decay function(s) Degree of a monomial, 338 Degree of a polynomial, 339 Dependent variable, 93 Depreciation rate, 304 Difference of two squares pattern, 384 Differences of consecutive y-values, 447 Diffusion coefficient, 283 Direct variation, 133 136, 153 defined, 134 identifying, 134 135 writing an equation for, 135 Discrete data, graphing, 100 Discrete domain, 100 Discrete function, 320 Discriminant, in Quadratic Formula defined, 506 interpreting, 506 507 Distance Formula, rate and time, 6, 30, 31 Distributive Property, 13 multiplying binomials using, 346 Division inequalities and negative numbers, 61 and positive numbers, 60 of integers, 1 linear equations, 5 polynomial long division, 358 359 of polynomials, 357 360, 397 Property of Equality, 5 of Inequality, 60, 61 Power of a Quotient, 280 Quotient of Powers, 279 Quotient, of Square Roots, 466 467 synthetic, 360 in units of measure, 2 Domain of a function continuous, 100 defined, 92 discrete, 100 E Elimination, using to solve systems of linear equations, 231 234, 269 Equation(s), See also Linear equation(s) approximating a solution of, 464 defined, 4 for a geometric sequence, 314 matching equivalent forms of, 363 multi-step, 11 15, 36 37 polynomial, in factored form, 363 366, 397 rewriting, 159 rewriting literal, 28 simple linear, 3 7, 36 with variables on both sides, 21 24, 37, 245 248 writing of parallel lines, 179 182, 211 of perpendicular lines, 179 182, 211 in point-slope form, 167 170, 210 in slope-intercept form, 161 164, 210 in standard form, 173 176, 210 211 Equivalent equations, 4 Equivalent inequalities, 54 Even function, 428 Explicit rule(s) defined, 320 translating to/from recursive rules, 322 Exponent properties, 277 281, 328 Exponential decay, 301 Exponential decay function(s), 299 302, 304, 329 defined, 301 Exponential function(s) comparing to quadratic and linear functions, 445 450, 458 defined, 292 exponential growth and decay, 299 304, 329 graphing, 293 294 identifying and evaluating, 291 292, 328 329 properties of exponents, 277 281, 328 radicals and rational exponents, 285 288, 328 writing using technology, 295 Exponential growth, 300 Exponential growth function(s), 299 303, 329 defined, 300 Exponential regression, 295 Expressions, evaluating, 87, 403 with rational exponents, 287 288 Extrapolation, 197 F Factored completely, 390 Factored form defined, 364 matching to standard forms, 389 of polynomial equations, 363 366, 397 Factoring difference of two squares, 384 perfect square trinomials, 385 polynomials, 364 366 ax 2 + bx + c, 377 380, 398 completely, 389 392, 398 by grouping, 390 special products, 383 386, 398 x 2 + bx + c, 371 374, 397 writing prime factorizations, 335 Factoring by grouping, 390 Factors and zeros, 438 Family of functions, 140 Fibonacci sequence, 323 FOIL Method, 347, 353 Formulas circle circumference, 27 radius, 64 cone radius, 290 volume, 27 cylinder, volume, 281, 394 defined, 29 Distance (rate, time), 6, 30, 31 Quadratic (See Quadratic Formula) quarterback passing efficiency, 53 rectangular prism, volume, 27 rewriting for surface area, 29 simple interest, 30, 31 sphere, radius, 288 temperature, 30 trapezoid, area, 27 Formulating a plan, 115 Four-step approach to problem, 6 Function(s), 89 93, 150 comparing linear, exponential, and quadratic, 445 450 comparing, using average rates of change, 448 449 constant, 126 defined, 89, 90 differences and ratios of, 447 domain and range, 92 exponential (See Exponential function(s)) family of, 140 finding zeros of, 437 438 A54
identifying, 89 independent and dependent variables, 93 linear (See Linear function(s)) parent, 140 quadratic (See Quadratic function(s)) relations and, 90 91 representations of, 99 Vertical Line Test, 91 zero of, 118 Function notation, 107 110, 151 defined, 107, 108 evaluating and interpreting, 108 graphing a linear function, 109 for independent variable, 109 G GCF, See Greatest common factor (GCF) Geometric sequence(s), 311 315, 330 common ratio, 312 defined, 312 equation for, 314 graphing, 313 nth term of, 314 writing as functions, 314 Golden ratio, 474 Golden ratio conjugate, 474 Golden rectangle, 469 Graph of an inequality, 48 Graph of a linear inequality, 252 Graph of a system of linear inequalities, 261 Graphing arithmetic sequences, 203 compound inequalities, 74 cubic functions, 440 exponential functions, 293 294 geometric sequences, 313 integers, 43 linear equations in slope-intercept form, 123 128, 152 in standard form, 115 119, 151 using intercepts, 117 from verbal description, 127 linear functions, 100 101, 217 continuous data, 100 101 discrete data, 100 matching functions with graphs, 107 using function notation, 109 linear inequalities, 45, 47 48, 80, 217 in one variable, 253 in two variables, 251 253, 270 points, 87 quadratic functions f(x) = (ax) 2, 408 f(x) = a(x p)(x q), 435 439 f(x) = a(x h) 2 + k, 427 431, 457 f(x) = ax 2, 405 408, 456 f(x) = ax 2 + bx + c, 417 421, 457 f(x) = ax 2 + c, 411 414, 456 parent function, 404, 406 using zeros, 438 equations by, 245 248, 270 quadratic equations by, 475 480, 515 systems of linear equations, 219 222, 268, 463 of linear inequalities, 259 263, 270 Graphing calculator exponential regression feature, 295 finding line of best fit, 193, 196 finding point of intersection, 218 intersect feature, 450, 505 linear inequalities in two variables, 251 linear regression feature, 196, 295 maximum feature, 421 quadratic regression feature, 480 inequality in one variable, 44 table feature, 315 trace feature, 197 viewing windows, standard and square, 88, 167 zero feature, 479 Graphs of an inequality, 48 of linear functions, transformations of, 139 144, 154 combining transformations, 143 144 comparing graphs of functions, 139 matching functions with graphs, 139 reflections, 141 shrinks, 142 143 stretches, 142 translations, 140 of linear inequality, 252 of system of linear inequalities, 261 using to write equations, 162 Greatest common factor (GCF) factoring out, 378 factoring polynomials using, 365 Greatest common monomial factor, 365 Growth, See Exponential growth function(s) H Half-planes, 252 Horizontal lines slope of, 175, 182 standard form of linear equation, 116 writing equations of, 175 Horizontal shrink defined, 142 graph of, 143 Horizontal stretch defined, 142 and shrinks, graph of, 142 Horizontal translations, 140 I Identity, 23 Inconsistent system, 238, See also No solutions Independent variable defined, 93 using function notation to solve, 109 of a radical, 286 Inequality(ies), See also Linear inequalities defined, 46 symbols for, 46, 47 Infinitely many solutions of linear equations, 23 in system of linear equations, 237 240 Input-output tables, 89, 99 Integers adding and subtracting, 1 multiplying and dividing, 1 Intercept form defined, of quadratic functions, 436 using to find zeros of functions, 435 440, 458 Interpolation, 197 Intersection (and), 74, 75 Inverse operations defined, 4 multiplication and division, 5 L Leading coefficient, 339 Like radicals, 470 Line(s) of best fit, 195 196 A55
Line(s) of fit analyzing, 193 197, 212 correlation and causation, 197 defined, 190 finding lines of best fit, 193, 195 196 and residuals, 194 195 and scatter plots, 187 190, 211 using to model data, 190 Linear equation(s) graphing in slope-intercept form, 123 128, 152 in standard form, 115 119, 151 using table of values, 403 identify special solutions of, 23 in one variable, defined, 4 real-life applications, 6 7 rewriting equations and formulas, 27 31, 38 in slope-intercept form, 126 127 by adding or subtracting, 4 equations with variables on both sides, 21 24, 37 by graphing, 245 248 by multiplying or dividing, 5 multi-step equations, 11 15, 36 37 simple equations, 3 7, 36 special solutions of, 23 standard form of, 116 steps for, 23 systems of (See System(s) of linear equations) Linear equation in two variables defined, 98 solution of, 100 Linear function(s) comparing to exponential and quadratic functions, 445 450, 458 graphing, 217 Linear functions, graphing about functions, 89 93 (See also Function(s)) about linear functions, 97 102 constant, 126 defined, 98 function notation, 107 110 graphing, 100 101 identifying, 98 99, 150 using equations, 99 using graphs, 98 using tables, 98 modeling direct variation, 133 136 transformations of graphs of, 139 144, 154 Linear functions, writing arithmetic sequences, 201 205 lines of fit, analyzing, 193 197 scatter plots and lines of fit, 187 190 writing, 163 writing equations of parallel and perpendicular lines, 179 182 in point-slope form, 167 170 in slope-intercept form, 161 164 in standard form, 173 176 Linear inequalities graphing, 45, 47 49, 80, 217 representing in words, algebra, and graphs, 49 compound inequalities, 73 76, 82 multi-step inequalities, 67 70, 81 using addition or subtraction, 53 56, 80 using multiplication or division, 59 62, 81 special solutions of, 69 systems of, 259 263, 270 writing, 45 46, 49, 80 Linear inequality(ies) in two variables defined, 252 graphing, 251 253, 270 writing, 251, 254 Linear model, 164 Linear regression defined, 195 finding line of best fit, 193, 195 on graphing calculator, 196, 295 Linear system, 220, See also System(s) of linear equations Literal equation, 28 Long division of polynomials, 358 359 M Mapping diagrams, 90, 99 Maximum value defined, 419 finding, of quadratic function, 419 421 by completing the square, 496 Measuring angles, 3 specifying units, 2 Minimum value defined, 419 finding, of quadratic function, 419 421 by completing the square, 496 Modeling direct variation, 133 136, 153 Modeling with Mathematics, Throughout. See for example: geometric sequences, 315 linear equations, 6, 7, 14 15, 24 linear functions, 161, 164, 176 linear inequalities, 53, 56, 76, 255 polynomials, 354, 366, 386 quadratic equations, 469, 498, 505 quadratic functions, 421, 431 systems of linear equations, 222, 228, 234, 239, 240, 247, 248 systems of linear inequalities, 263 Monomial(s) defined, 338 dividing polynomials by, 358 multiplication of, 345 Multiplication inequalities and negative numbers, 61 and positive numbers, 60 of integers, 1 linear equations, 5 of polynomials, 345 348, 396 Property of Equality, 5 of Inequality, 60, 61 Power of a Power, 279, 286 Power of a Product, 280 Product of Powers, 279 Product, of Square Roots, 466 of radicals and square roots, 465, 470 in units of measure, 2 Multi-step equations combining like terms to solve, 12, 12 13 a two-step equation, 12 using structure to solve, 13 using unit analysis on real-life problems, 15 writing a multi-step equation, 11 Multi-step inequalities,, 67 70, 81 N Negative Exponents Property, 278 Negative numbers, multiplying or dividing inequalities, 61 No solutions of linear equations, 23 in system of linear equations, 237 238 in system of linear inequalities, 261 Nonlinear function(s), 98 A56
Notation functions, 107 110, 151 standard, 107 nth root of a, 286 nth roots, 285 287 nth term of arithmetic sequences, 204, 275 of geometric sequence, 314 Number line, 7 describing intervals on, 73 graphing numbers on, 43 O Odd function, 428 or (union), 74, 75 Order of operations, 275 Ordered pairs, 90 P Parabola, 406 Parallel lines defined, 180 writing equations of, 179 182, 211 Parent function, 140 Parent quadratic function, 404, 406 Pascal s Triangle, 326 Patterns arithmetic sequences, 201 difference of two squares pattern, 384 geometric sequences, 311 in horizontal and vertical translations, 140 Pascal s Triangle, 326 perfect square trinomial pattern, 385 recursively defined sequences, 319 for similar figures, 97 square of binomial pattern, 351 352 sum and difference pattern of polynomials, 351, 353 writing rules, 59 Perfect square trinomial pattern, 385 Perfect square trinomials completing the square, 494 factoring, 463 Performance Tasks Any Beginning, 209 Asteroid Aim, 455 The Cost of a T-Shirt, 149 Form Matters, 513 Grading Calculations, 79 Magic of Mathematics, 35 The New Car, 327 Prize Patrol, 267 The View Matters, 395 Perimeter, equations with variables on both sides, 21 Perpendicular lines defined, 181 writing equations of, 179 182, 211 Point-slope form defined, 168 writing equations in, 167 170, 210 Polygons, for angle measures of, 11, 16 Polynomial(s) adding and subtracting, 337, 340 341, 396 classifying, 339 defined, 339 degrees of monomials, 338 dividing, 357 360, 397 factoring ax 2 + bx + c, 377 380, 398 completely, 389 392, 398 by grouping, 390 special products, 383 386, 398 x 2 + bx + c, 371 374, 397 multiplying, 345 348, 396 special products of, 351 354, 383 386, 396, 398 in standard form, 339 Polynomial equations, in factored form, 363 366, 397 Polynomial long division, 358 359 Positive numbers, multiplying or dividing inequalities, 60 Power of a Power Property, 279, 286 Power of a Product Property, 280 Power of a Quotient Property, 280 Powers, 279 280 Precise Mathematical Language communication and symbols, 45 definitions and symbols, 107 table of values and graphing, 438 viewing window for graphs, 196 Predictions, of future events with growth pattern, 299 Prime factorizations, 335 Problem Solving, Throughout. See for example: common strategies, 7 finding a pattern, 276 four-step approach to, 6 graphing parent quadratic function, 404 guess, check, and revise strategy, 464 using a strategy, 160 Product of Powers Property, 279 Product Property of Square Roots, 466 Properties Addition Property of Equality, 4 Addition Property of Inequality, 54 Distributive Property, 13 Division Property of Equality, 5 Multiplication and Division Properties of Inequality, 60, 61 Multiplication Property of Equality, 5 Negative Exponents, 278 Power of a Power, 279, 286 Power of a Product, 280 Power of a Quotient, 280 Product of Powers, 279 Product Property of Square Roots, 466 Quotient of Powers, 279 Quotient Property of Square Roots, 466 467 Subtraction Property of Equality, 4 Subtraction Property of Inequality, 55 Zero Exponent, 278 Zero-Product Property, 364 Punnett square and gene combinations, 354, 356 Q Quadratic equation(s) approximating solutions of, 487 defined, 476 methods for, summary of, 507 number of solutions of, 476 477 properties of radicals, 465 470, 514 by completing the square, 493 498, 508, 516 by factoring, 508 by graphing, 475 480, 515 using Quadratic Formula, 503 508, 516 using square roots, 485 488, 515 Quadratic Formula defined, 504 deriving, 503 interpreting the discriminant, 506 507 quadratic equations using, 503 508, 516 Quadratic function(s) characteristics of, 406 comparing to linear and exponential functions, 445 450, 458 defined, 406 even and odd functions, 428 A57
graphing f(x) = (ax) 2, 408 f(x) = a(x p)(x q), 435 439 f(x) = a(x h) 2 + k, 427 431, 457 f(x) = ax 2, 405 407, 456 f(x) = ax 2 + bx + c, 417 421, 457 f(x) = ax 2 + c, 411 414, 456 parent function, 404 using zeros, 438 interpreting forms of, 497 using intercept form to find zeros, 435 439, 458 Quadratic regression, 480 Quadrilaterals, measuring angles of, 3, 8 Quotient of Powers Property, 279 Quotient Property of Square Roots, 466 467 R Radical(s) adding and subtracting, 470 defined, 286 multiplying, 470 properties of, 465 470, 514 Product Property of Square Roots, 466 Quotient Property of Square Roots, 466 467 roots and rational exponents, 285 288, 328 Radical expression, 466 Radicand, 287 Range of a function, 92 Rational exponents, 287 288 Rationalizing the denominator, 468 Ratios of functions, and differences, 447 Reading causal relationship, 197 ellipsis, 202 function notation, 108 if and only if, 180 inequalities, 46, 252 linear system, 220 nth roots, 286 solutions of an identity, 23 subscripts, 124 Real nth roots of a, 286 Real-life problems, Throughout. See for example: exponential functions bacteria populations, 294 beach ball radius, 288 car depreciation, 304 compound interest, 303 volume of cylinder, 281 inequalities electric circuit, 56 electrical devices and temperature, 76 hourly wage, 62 trivia game, 70 linear equations multi-step, 14 using Distance (rate, time) Formula, 31 using unit analysis to model, 15 with variables on both sides, 24 linear functions artist s profit, 118 cable fees, 144 discrete or continuous, 102 elevation of submersible, 128 fish tank and salt, 136 helicopter distance, 110 table seatings, 119 linear inequalities and prices of fruit, 255 linear models arithmetic sequences, 205 function types, comparing, and populations, 450 possible combinations, 176 renewable energy, 164 school spirit, 170 polynomials arch of fireplace, 366 falling distance and time, 341, 386 hockey trapezoidal region, 348 land area, 374, 380 Punnett square and gene combinations, 354, 356 terrarium as rectangular prism, 392 problem four-step approach to, 6 strategies, 7 quadratic equations dimensions of touch tank, 488 height of football, 479 height of rocket, 497 quadratic functions falling object, 414 satellite dish, 408 water fountains, 431 radical equations and horizon distance, 469 systems of linear equations and car rental, 248 cost of delivery vans, 234 drama club tickets, 228 fish populations, 247 perimeter of land, 240 renting banquet halls, 239 roofing shingles, 222 teacher salaries, 234 systems of linear inequalities and time to spend, 263 Reasoning Throughout. See for example: compound inequalities, 73 linear equations, 23 quantities and relationships, 187 representation of problem, 73 unit analysis, 27 using formulas, 27 Rectangular prism, volume, 27 Recursive Equation, 319 for an Arithmetic Sequence, 320 for a Geometric Sequence, 320 Recursive rule(s) defined, 320 translating to/from explicit rules, 322 writing, 321, 323 Recursively defined sequences, 319 323, 330 writing recursive rules, 321 writing terms of, 320 Reflection(s) defined, 141 in x-axis, 141 in y-axis, 141 Regression exponential, 295 linear, 193, 195, 196, 295 quadratic, 480 Regular dodecahedron, volume, 290 Relation(s) defined, 89, 90 functions and, 90 91 Remember approximately equal symbol, 6 compatible numbers, 62 compound inequality with and, 74 constant rate of change, 98 distance formula, 6 division by 0, 28 dollars per person, 15 domain and range, 419 domain of set, 205 f(x) notation, 406 functions, 163 functions/zeros and graphs/x-intercepts, 437 functions/zeros, graphs/x-intercepts, equations/solutions, 479 A58
inequality solution, 54 inverse operations, 5 linear equations, 221 mapping diagram, 90 mean, 70 miles per day, 15 negative reciprocal, 181 number line, 7 power and exponents, 279 quadratic functions, stretch, shrink, and reflection, 407 quadratic functions, translations, 412 radicand, 287 scientific notation, 281 slopes of horizontal and vertical lines, 182 x-intercept, 127 Repeated roots, 365 Residual(s), 194 195 Rise, 124 Roots, 364 Roots, nth, 285 287 Rule defined, 3 for properties of exponents, 277 writing inequalities, 59 Run, 124 S Scatter plots defined, 187, 188 and lines of fit, 187 190, 211 Scientific notation, 281 Sequence(s) arithmetic, 201 205, 212 defined, 202 Fibonacci, 323 geometric, 311 315, 330 recursively defined, 319 323, 330 Set-builder notation, 48 Shrinks, 142 143 Simple interest, formula for, 30, 31 Simplest form, 466 Slope, and points, See Point-slope form Slope-intercept form defined, 126 graphing linear equations in, 123 128, 152 writing equations in, 161 164, 210 Slope of line defined, 123, 124 finding, 123 125 of horizontal and vertical lines, 175, 182 identifying slopes and y-intercepts, 126 positive, negative, 0, and undefined, 125 Solution(s) defined, 4 number from linear equations, 23 number from linear systems, 238 number from quadratic equation, 477 Solution of an inequality, 47 Solution of a linear equation in two variables, 100 Solution of a linear inequality in two variables, 252 Solution set, 47 Solution of a system of linear equations, 220 Solution of a system of linear inequalities, 260 Sphere radius, 288 volume, 290 Square of binomial pattern, 351 352 Square roots finding, 275 operations with, 465 Product Property of, 466 Quotient Property of, 466 467 quadratic equations using, 485 488, 515 Standard form defined, 116 graphing linear equations in, 115 119, 151 of polynomials defined, 339 matching to factored form, 363, 389 writing equations in, 173 176, 210 211 Stretches, 142 Structure, a multi-step equation, 13 Study Skills Analyzing Your Errors Application Errors, 65 Misreading Directions, 309 Study Errors, 243 Completing Homework Efficiently, 19 Getting Actively Involved in Class, 185 Keeping a Positive Attitude, 491 Learning Visually, 425 Preparing for a Test, 369 Staying Focused during Class, 113 Substitution, using to solve systems of linear equations, 225 228, 268 Subtraction of integers, 1 linear equations, 4 linear inequalities, 55 of polynomials, 337, 340 341, 396 Property of Equality, 4 of Inequality, 55 of radicals and square roots, 465, 470 in units of measure, 2 Sum and difference pattern, 351, 353 Symbols approximately equal to, 6 for inequality, 46, 47, 251 Symmetric about the origin, 428 Symmetry, See Axis of symmetry Synthetic division, 360 System(s) of linear equations defined, 219, 220 by elimination, 231 234, 269 equations by graphing, 245 248 by graphing, 219 222, 268, 463 special systems, 237 240, 269 by substitution, 225 228, 268 writing, 219 System(s) of linear inequalities defined, 260 graphing and writing, 259 263, 270 T Technology, See Graphing calculator Temperature compound inequalities of, 76 formula for, 30 Term(s) arithmetic sequences, finding the nth term of, 204 defined, 202 writing for arithmetic sequences, 202 Theorem, 3 Transformation(s) defined, 140 of graphs of linear functions, 139 144, 154 combining transformations, 143 144 reflections in x-axis and y-axis, 141 shrinks, 142 143 stretches, 142 translations, horizontal and vertical, 140 of graphs of parent quadratic functions, 406 A59
of graphs of quadratic functions, 430 Translation(s) defined, 140 horizontal, 140 vertical, 140 Trapezoid, area, 27 Trend line, 190 Triangle, equilateral, area of, 488 Trinomial(s) defined, 339 factoring x 2 + bx + c, 371 374, 397 multiplying with a binomial, 348 U Union (or), 74, 75 Unit analysis, 15 Units of measure, 2 V Variables independent and dependent, 93 equations with variables on both sides, 21 24 Vertex in quadratic function comparing x-intercepts with, 417 defined, 406 finding axis of symmetry and, 418 Vertex form of quadratic function, 430 Vertical Line Test, 91 Vertical lines slope of, 175, 182 standard form of linear equation, 116 writing equations of, 175 Vertical shrink defined, 142 graph of, 143 of quadratic function, 407 Vertical stretch defined, 142 of quadratic function, 407 and shrinks, graph of, 142 Vertical translations, 140 Volume formulas of cone, 27 of cylinder, 281, 394 of rectangular prism, 27 regular dodecahedron, 290 sphere, 290 W Writing, Throughout. See for example: compound inequalities, 74 linear inequalities, 45 46, 49 linear inequalities in two variables, 251, 254 rewriting equations and formulas, 27 31 rules for inequalities, 59 system of linear inequalities, 262 X x-axis reflections, 141 x-intercept comparing with vertex, 417 defined, 115, 117 finding number for parabola, 507 using to graph linear equations, 117 Y y-axis reflections, 141 y-intercept defined, 115, 117 finding slopes and, 123 identifying slopes and, 126 using to graph linear equations, 117 using to write equations, 162 Z Zero Exponent Property, 278 Zero of a function defined, 118 in falling object problem, 414 finding and approximating, 478 using intercept form, 435 440, 458 Zero-Product Property, 364 A60