Direct variation, 475–476
as a power, 476
Discriminant of quadratic formula, 570
Distance, rate, and time relationship,
143–144, 230, 275, 468
Distance formula, 499
for falling objects, 392
Distributive property, 64
Dividend, 51
Divisibility tests for numbers, 58, 360
Division
of complex numbers, 577
of decimals, 134
definition of, 51
of fractions, 5
long, 342–343
in order of operations, 16
of polynomials, 340–342
of radicals, 507
of rational expressions, 430
of real numbers, 51, 59
of signed numbers, 52, 59
word phrases for, 54–55
involving zero, 52
Divisor, 51
Domain, 229, 232
of a quadratic function, 583
Double negative rule, 32
Double solution, 396
Earthquake, intensity of, 315
Elements of a set, 25, 597
Elimination method
for solving dependent equations, 268
for solving inconsistent systems, 268
for solving linear systems, 264
steps to solve by, 265
Empty set, 103, 597
symbols for, 103, 597
Equal sets, 598
Equality
addition property of, 87
multiplication property of, 92
squaring property of, 531
Equation(s), 24, 86.See alsoSystem of
linear equations
conditional, 102–103
dependent, 251
for depreciation, 197
distinguishing from expressions, 25, 456
equivalent, 86
extraneous solution of, 532
from sentences, 55–56
graph of, 188
of a horizontal line, 192
independent, 251
linear in one variable, 86
linear in two variables, 177, 191
literal, 123
with no solutions, 532
quadratic, 324, 392, 554
with radicals, 531
with rational expressions, 456
simplifying, 89, 95
slope of, 204
solution set of, 86
solutions of, 24, 86
square root property of, 554
of a vertical line, 193
Equation of a line, 211
point-slope form of, 213–214
slope-intercept form of, 211
standard form of, 215
Equilibrium demand, 256
Equilibrium supply, 256
Equivalent equations, 86
Equivalent forms for a rational
expression, 424–425
Even consecutive integers, 113, 401
Exponential expressions, 15, 296
base of, 15, 296
evaluating, 15
Exponents, 15, 296
application of, 312
fractional, 540
integer, 303
negative, 303–304
in order of operations, 16
positive, 305–306
power rules for, 298–299
product rule for, 296–297
quotient rule for, 306
rational, 540
and scientific notation, 312
summary of rules for, 299, 307
zero, 304
Expressions
algebraic, 22
distinguishing from equations, 25, 456
exponential, 15, 296
from word phrases, 72
quadratic, 392
radical, 494
rational, 420
simplifying, 69–70
terms of, 70–71, 320
Extraneous solution, 532
Extremes of a proportion, 131Factoring, 360
difference of cubes, 384
difference of squares, 381
with four terms by grouping, 363–364
greatest common factor, 360
by grouping, 363
guidelines for, 370
perfect square trinomials, 382
sum of cubes, 386
Factoring method for solving quadratic
equations, 392, 554Factoring trinomials, 368
by grouping, 373
in two variables, 377
using FOIL, 368, 375
Factors, 2, 360
common, 360
greatest common, 3, 360
of integers, 50
of a number, 2, 360
prime, 2
Fahrenheit-Celsius relationship, 124
Fibonacci, 494
Finite set, 597
distinguishing from infinite, 598
First-degree equation.SeeLinear
equations
Fixed cost, 220
FOIL, 331, 368, 375
inner product of, 331
outer product of, 331
Formulas
to evaluate variables, 120
geometry, 120
Fourth power(s)
perfect, 499
Fourth root, 499
symbol for, 499
Fraction bar, 2, 16, 17
Fractional exponents, 540
definition of, 540
rules for, 541
Fraction(s), 2
basic principle of, 3
complex, 448
denominator of, 2
improper, 2
least common denominator of, 6, 435
linear equations with, 100–101
linear systems with, 261
lowest terms of, 3
mixed numbers, 7
numerator of, 2
operations on, 4–8
proper, 2
quadratic equations with, 571
reciprocals of, 5, 51, 63
Function, 230, 399
domain of, 232
input-output, 230
linear, 235
notation, 233
quadratic, 583
range of, 232
vertical line test for graph of, 231
Fundamental property of rational
expressions, 422
notation, 233Galileo Galilei, 392, 399
Geometry applications, 120G
ƒ 1 x 2F
E
I-2 Index
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