Index Index
\(\Delta\). See Delta
absolute value, Assemblage Reading Question
addition, Subsection
commutative law of, Assemblage
of fractions, Subsection Assemblage Assemblage Assemblage Subsection Assemblage
of integers, Assemblage
of radicals, Subsection Assemblage
of signed numbers, Assemblage
rules for adding integers, Assemblage
algebraic expression, Assemblage Assemblage
evaluating, Subsection Assemblage Subsubsection Subsection
with graphs, Paragraph
simplifying, Subsection
writing, Subsection Assemblage Subsubsection Subsection
algebraic fraction, Subsection Assemblage. See also fractions
applications, Subsection
binomial divided by opposite, Assemblage
reducing, Subsection Assemblage Assemblage
applied problems, Assemblage Subsection Subsection
area, Assemblage. See also surface area
of rectangle, Paragraph
associative law
for addition, Assemblage
for multiplication, Assemblage
average
formula for, Assemblage
axis, Assemblage Subsection Subsection
choosing scale for, Subsection Subsubsection
b as \(y\)-intercept, Assemblage
base
exponent and, Assemblage Assemblage
binomial, Item
difference of two squares, Assemblage
multiplying, Subsection
product of, Section
square of, Subsection Assemblage
box method for factoring a quadratic trinomial, Subsection Assemblage Subsection Assemblage
build (a fraction). See fractions
building factor, Item. See also fractions
building fractions, Assemblage. See also fractions
canceling to reduce a fraction, Assemblage Caution Assemblage Caution Assemblage Caution Caution. See also fundamental principle of fractions
Cartesian coordinate system, Subsection Paragraph
change in. See Delta
coefficient, Assemblage
of linear equation, Assemblage
of quadratic equation, Paragraph
combining like terms, Paragraph. See also like terms
commutative law
of addition, Assemblage
of multiplication, Assemblage
complex number, Paragraph
compound inequality, Subsection
consistent and independent, Paragraph
consistent system of equations, Assemblage
constant of proportionality, Assemblage
counting number, Paragraph
cross-multiply. See proportion
cube, Subsection
cube root, Subsection Assemblage Assemblage
equation, Subsection (see also equation)
degree (of a polynomial), Subsection Paragraph
Delta (\(\Delta\)), Assemblage
dependent system of equations, Subsection Paragraph Assemblage Subsection Assemblage
difference, Subsection Paragraph. See also subtraction
of two squares, Assemblage
directed distance, Assemblage Assemblage
distance
between points, Subsection
directed, Assemblage Assemblage
formula for, Assemblage
distributive law, Section Subsection Assemblage
with algebraic expressions, Subsection
division
involving zero, Subsection Assemblage
not commutative, Assemblage
of fractions, Subsection Assemblage Assemblage
of monomials, Subsection
of polynomials, Subsection
of signed numbers, Subsection Assemblage
elimination method, Paragraph. See also system of equations
equation, Assemblage Assemblage
clearing fractions, Subsection Subsection
first-degree, Paragraph
graph of, Assemblage Subsection Assemblage Assemblage Subsection
of line (see linear equation)
of parabola (see quadratic equation)
problem solving with, Subsection
solution of, Section Assemblage
algebraically, Assemblage Assemblage Subsubsection
with graphs, Subsection Paragraph
with \(x^2\), Subsection (see also quadratic equation)
with cube roots, Subsection
with radicals, Subsection Assemblage Assemblage
writing, Subsubsection
equivalent, Assemblage
expressions, Subsection Assemblage
evaluating
an algebraic expression, Subsection Assemblage
evaluating an algebraic expression, Subsubsection. See also algebraic expression
exponent, Subsection Assemblage Assemblage Assemblage
fifth law, Assemblage
first law, Assemblage Assemblage
fourth law, Assemblage
laws of, Section Assemblage Assemblage
negative, Section Subsection Assemblage Assemblage
second law, Assemblage Assemblage
third law, Assemblage
zero, Subsection Assemblage
expression, Subsection Assemblage
equivalent, Subsection Assemblage
simplifying, Assemblage
extraction of roots, Subsection Assemblage Subsection
extraneous solution, Subsection Paragraph Assemblage Paragraph Subsection Assemblage
factor, Paragraph Assemblage Assemblage Assemblage. See also factoring
building, Subsection (see also fractions)
factored form, Paragraph
factoring, Subsection Paragraph Section Subsection
difference of squares, Assemblage
perfect square trinomial, Assemblage
quadratic trinomials, Subsection Assemblage Assemblage Subsection
solve equations by, Subsection Assemblage
special factorizations, Assemblage
sum of two squares, Assemblage
the box method, Assemblage
first-degree, Paragraph. See also linear
FOIL (terms of binomial product), Subsection Assemblage Paragraph Assemblage Assemblage
formula, Assemblage
solving for a variable (with quadratic term), Subsection
solving for one variable, Subsection Example
solving formula with algebraic fractions for a variable, Subsection
using, Subsubsection
fractions
adding and subtracting, Subsection Assemblage Assemblage Subsection Assemblage
unlike, Subsection Assemblage
algebraic (see algebraic fraction)
building, Subsection
clearing, Subsection (see also equation)
dividing, Subsection Assemblage Assemblage
involving square roots, Subsection (see also rationalizing the denominator)
multiplication shortcut, Assemblage
multiplying, Subsection Assemblage Assemblage
products of, Subsection Assemblage Assemblage
quotient of, Subsection Assemblage Assemblage
reducing, Subsection Assemblage Assemblage
solving equations with variable in denominator, Subsection
standard form for writing negative fraction, Assemblage Assemblage
fundamental principle of fractions, Assemblage Assemblage
GCF. See greatest common factor
graph, Section Subsection
of an equation, Assemblage Subsection Assemblage Assemblage Subsection
of quadratic equation, Subsection (see also parabola)
graphing. See graph
greatest common factor, Subsection Assemblage
guess-and-check method for factoring, Subsection
horizontal axis. See \(x\)-axis
horizontal line, Subsection
equation of, Assemblage
hypotenuse, Paragraph
inconsistent system of equations, Subsection Paragraph Assemblage Subsection Assemblage
independent system of equations, Assemblage
inequality, Assemblage
compouind, Subsection
solving, Subsection Assemblage Subsection Subsection
input
variable, Assemblage Subsection
integer, Assemblage
rules for adding, Assemblage
rules for subtracting, Assemblage
intercept, Section. See also x-intercept
finding intercepts of a graph, Assemblage
interpreting, Subsection
method of graphing, Subsection Assemblage
of a line, Assemblage
interest, Subsection
formula for, Assemblage
inverse operations, Subsection Assemblage Assemblage Subsubsection
irrational number, Assemblage
LCD. See lowest common denominator
leg (of a right triangle), Paragraph
like radicals, Assemblage
like terms, Subsection Assemblage Subsection
adding and subtracting, Subsection Assemblage Assemblage Assemblage
combining, Subsection Assemblage
involving exponents, Subsection
linear combination, Assemblage Paragraph. See also system of equations
linear equation, Assemblage
coefficients, Assemblage
finding, Subsection Assemblage
graph of, Subsection
point-slope formula, Assemblage
writing, Subsection
lines
horizontal, Subsection Assemblage
parallel, Paragraph Assemblage Assemblage
perpendicular, Paragraph Assemblage
properties of, Section
vertical, Subsection Assemblage
lowest common denominator, Section Item Subsection Assemblage
clearing fractions, Subsection
finding, Assemblage
m as slope, Paragraph Assemblage
mathematical sentence, Item Assemblage Subsubsection
mixtures, Subsection. See also percent
monomial, Item
square of, Subsection
motion problems, Subsection
multiplication
commutative law of, Assemblage
of signed numbers, Subsection Assemblage
multiplying
binomials, Subsection
by a monomial, Subsection
by a power of ten, Assemblage Subsection
fractions, Subsection Assemblage Assemblage
polynomials, Section Subsection
radicals, Subsection
natural number, Paragraph
negative
\(\Delta x\), Item
\(\Delta y\), Item
of a binomial, Subsection Assemblage
slope, Subsubsection
negative exponent. See exponent
negative numbers, Paragraph
negative reciprocal, Assemblage
non-real, Item
solutions, Subsection
number line, Paragraph
adding numbers with the opposite signs, Subsection
adding numbers with the same sign, Subsection
subtracting a negative number, Subsection
subtracting a positive number, Subsection
numerical coefficient, Assemblage. See also coefficient
opposite of a binomial, Subsection Assemblage
opposite operations. See inverse operations
order of operations, Section Assemblage Assemblage Assemblage
addition, Subsection
division, Subsection
fraction bars, Assemblage
multiplication, Subsection
parentheses, Assemblage
powers, Assemblage
subtraction, Subsection
summary, Assemblage
with calculator, Subsubsection
with radicals, Assemblage
order symbol, Assemblage Assemblage. See also inequality
ordered pair, Assemblage
origin, Subsection
output
variable, Assemblage Subsection
parabola, Subsection Subsection Paragraph
graphing, Assemblage
vertex, Subsection Assemblage Assemblage
parallel lines, Paragraph
parentheses
removing, Subsection Assemblage Assemblage
percent, Subsection
formula for, Assemblage
perfect square, Paragraph
perpendicular lines, Paragraph Assemblage
point-slope formula, Section Assemblage
polynomial, Chapter Subsection Assemblage
adding, Subsection
division, Subsection
evaluating, Subsection
multiplying, Subsection
subtracting, Subsection
positive
\(\Delta x\), Item
\(\Delta y\), Item
positive numbers, Paragraph
power, Assemblage Assemblage. See also exponent
of a power, Subsection (see also exponent)
of a product, Subsection (see also exponent)
of a quotient, Subsection (see also exponent)
of a variable, Subsection Assemblage
of negative number, Subsection Assemblage
of ten, Subsection Assemblage
principal square root, Paragraph
product, Subsection. See also multiplication
of algebraic expressions, Subsection
of binomials, Section
of fractions, Subsection Assemblage Assemblage
of monomials, Subsection
of polynomials, Section Subsection Assemblage Subsection
of signed numbers, Subsection Assemblage
of variables, Subsection (see also power)
product rule. See radical
profit
formula for, Assemblage
properties of equality
addition and subtraction, Assemblage
multiplication and division, Assemblage
proportion, Subsection Assemblage Assemblage
cross-multiply, Assemblage
property of, Assemblage
proportional variables, Subsection Assemblage Assemblage
constant of proportionality, Assemblage
equation for, Assemblage
Pythagorean Theorem, Subsection Assemblage
quadrant, Subsection
quadratic, Subsection. See also equation; polynomial
solve by extraction of roots, Assemblage
quadratic equation, Paragraph Paragraph Subsection Assemblage
graph of, Subsection (see also parabola)
graphing, Assemblage
nature of solutions, Assemblage
solve by factoring, Subsection Assemblage Subsection Assemblage
solving, Subsection
quadratic formula, Section Assemblage
quadratic trinomial, Item
in two variables, Subsection
quotient, Subsection. See also division
involving zero, Subsection Assemblage
of fractions, Subsection Assemblage Assemblage
of monomials, Subsection
of powers, Subsection
of signed numbers, Subsection Assemblage
quotient rule. See radical
radical, Subsection Paragraph
adding, Subsection Assemblage
equation, Subsection Assemblage Assemblage
like, Assemblage
multiplying, Subsection
operations on, Section
product rule, Subsection Assemblage Assemblage
quotient rule, Subsection Assemblage Assemblage
subtracting, Subsection Assemblage
radical sign (\(\sqrt{\hphantom{1} \vphantom{1}} \thinspace \)), Paragraph
radicand, Paragraph
rate, Assemblage Assemblage
of change, Subsection Assemblage
ratio, Subsection Paragraph Assemblage
rational expression, Assemblage. See also algebraic fraction
rational number, Assemblage
decimal form, Assemblage
rationalizing the denominator, Subsection
real line, Assemblage. See also number line
real number, Assemblage
revenue, Subsection Assemblage
right
triangle, Paragraph
roots, Section. See also radical
cube, Section Subsection Assemblage Assemblage (see also cube root)
extraction of, Section (see also quadratic equation)
square, Section (see also square root)
satisfy an equation or inequality, Paragraph
scientific notation, Subsection Assemblage
mental calculation with, Subsection
writing in, Assemblage
second-degree, Paragraph. See also quadratic
signed number, Section
addition of, Assemblage
division of, Subsection Assemblage
multiplying, Subsection Assemblage
subtraction of, Assemblage
simplifying an expression, Assemblage
slope, Assemblage
calculate, Subsubsection
compute, Subsubsection
formula for, Assemblage Assemblage
meaning, Subsection Assemblage Subsection
negative, Subsubsection
of vertical line, Item
vertical line, Assemblage
slope-intercept form, Section Assemblage
finding, Subsection
method for graphing, Subsection (see also slope-intercept method)
slope-intercept method, Subsection Assemblage
solution
extraneous (see extraneous solution)
of equation, Assemblage
to a system of equations, Assemblage Section
to an equation in two variables, Assemblage
solving an equation, Assemblage Subsection. See also equation
solving an inequality, Assemblage Subsection
square, Paragraph
perfect, Paragraph
square root, Assemblage Assemblage. See also radical
involving fractions, Subsection (see also rationalizing the denominator)
of variable expression, Subsection
principal, Paragraph
simplifying, Subsection Assemblage
undefined, Assemblage (see also complex number)
standard form
of writing negative fractions, Assemblage
subscript, Paragraph Assemblage
subscript notation, Subsection Assemblage
substitution method, Subsection. See also system of equations
subtraction, Subsection
not commutative, Assemblage
of fractions, Subsection Assemblage Assemblage Subsection Assemblage Subsection Assemblage
of integers, Assemblage
of radicals, Subsection Assemblage
of signed numbers, Assemblage
rules for adding integers, Assemblage
sum, Subsection Paragraph. See also addition
of two squares, Assemblage
surface area, Subsection Assemblage
formulas, Subsection
system of equations
algebraic solution, Section
consistent and independent, Assemblage
dependent, Subsection Paragraph Assemblage Subsection Assemblage
inconsistent, Subsection Paragraph Assemblage Subsection Assemblage
problem solving with, Section
solve by elimination, Assemblage
solve by graphing, Subsection
solve by linear combinations, Assemblage
solve by substitution method, Assemblage
system of linear equations, Section Assemblage. See also system of equations
solution, Assemblage
term, Paragraph
like, Subsection
of the sum, Paragraph
trial and error, Subsection
trinomial, Item. See also factoring; quadratic trinomial
two-point formula for slope, Assemblage
undefined
division by zero, Paragraph Assemblage
quotient, Paragraph Assemblage
slope of vertical line, Assemblage
variable, Subsection Assemblage
vertex of a parabola, Subsection Assemblage Assemblage
vertical axis. See \(y\)-axis
vertical line, Subsection
equation of, Assemblage
volume, Subsection Assemblage
formulas, Subsection
of box, Paragraph
whole number, Paragraph
y-axis, Subsection
y-intercept, Assemblage
zero
as an exponent, Subsection Assemblage (see also exponent)
zero-factor principle, Subsection Assemblage Subsection