Index Index
absolute value
solving equations with one absolute value, Fact
solving equations with two absolute values, Fact
Addition
associative property of, Paragraphs List
commutative property of, Paragraphs List
identity property of, Paragraph
inverse property of, Paragraph
addition
of polynomials, Subsection
Addition method for system of linear equations. See Elimination method
Addition property
of equality, Fact
of inequality, Paragraph
Additive identity, Paragraph
Additive inverse, Paragraph
Algebraic expression, Paragraph
evaluating, Example
simplifying, Example
Algebraic expressions
simplifying, Paragraph
Algebraic translations of English phrases, Paragraph
area, Paragraphs
Associative property, Paragraphs
of addition, List
of multiplication, List
Axis
horizontal, Definition
vertical, Definition
axis of symmetry, Paragraph
Cartesian coordinate system, Paragraph Definition
René Descartes, Section
circumference, Paragraphs
coefficient, Definition
Combining like terms, Subsection Paragraphs
Commutative property, Paragraphs
of addition, List
of multiplication, List
complex fraction, Paragraph
complex number, Definition
compound inequality, Definition
or, Paragraph
conjugates, Paragraph
constant polynomial, Item
constant term, Definition
Coordinate plane, Definition
Coordinates, Definition
of a point, Section
cubic polynomial, Item
degree
of a polynomial, Definition
of a term, Definition
Dependent equations, Paragraph
Dependent system, Paragraph
discriminant, Paragraph
Distributive property, Paragraphs List
dividing a polynomial by a monomial, Subsection
Division property of equality, Fact
domain, Definition
Elimination method
for system of linear equations, Subsection
systems having infinitely many solutions, Example
systems having no solution, Example
English phrases and sentences
algebraic translations of, Paragraph
Equation
linear, Definition
equation
quadratic, Definition
radical, Definition
rational, Definition
Equation of a line
horizontal line, Paragraph
point-slope form, Definition
slope-intercept form, Definition
standard form, Definition
vertical line, Example
Equation(s), Paragraph
addition property of equality for solving, Fact
dependent, Paragraph
equivalent, Paragraph
inconsistent, Paragraph
multiplication property of equality for solving, Fact
solution of, Definition
solution set of, Paragraph
translating to, Paragraph
using both addition and multiplication properties, Subsection Process
with fractions, Paragraph
Equations in two variables
graphing, Paragraph
linear, Definition
Equivalent equations, Paragraph
Evaluating algebraic expressions, Example
exponent, Paragraph
base, Paragraph
introductory rules, List
negative integer, Definition
power, Paragraph
power to a power rule, Paragraph
product rule, Paragraph
product to a power rule, Paragraph
quotient of powers property, Fact
quotient to a power rule, Fact
zero, Definition
Expression
algebraic, Paragraph
linear, Paragraph
extraneous solution, Remark
extraneous solutions, Remark
factored form of a quadratic function, Fact
factoring
by grouping, Subsection
by the AC method, Subsection
decision tree, Section
difference of squares, Subsection
in stages, Subsection
perfect square trinomials, Subsection
trinomials with higher powers, Subsection
with factor pairs, Subsection
Factors, Paragraph
FOIL, Paragraphs
Formulas, Paragraph
Fraction
clearing denominators, Paragraph
linear equations with, Paragraph
function
domain, Definition
informal definition, Definition
range, Definition
technical definition, Definition
G.C.F., Paragraph
generic rectangle, Paragraph
Graph
of an equation, Paragraph
of an inequality, Example
Graphing
equations in two variables, Paragraph
intercepts, Example
linear equations in two variables, Paragraph
lines in slope-intercept form, Figure
solution set to an inequality, Example
systems of linear equations, Subsection
Graphs
of inequalities, Figure
Greater-than symbol, Paragraph
Greater-than-or-equal-to symbol, Paragraph
greatest common factor, Paragraph
horizontal asymptote, Remark
horizontal intercept, Paragraph
Horizontal line, Paragraph
slope of, Example
Identity, Subsection
additive, Paragraph
multiplicative, Paragraph
Identity property
of addition, Paragraph
of multiplication, Paragraph
imaginary numbers, Definition
imaginary unit, Definition
Inconsistent equations, Paragraph
Inconsistent system, Paragraph
index, Definition
Inequalities, Paragraph
graphing, Example
solution sets of, Example
solutions of, Definition
with infinitely many solutions, Example
with no solutions, Example
Inequality
linear, Definition
Intercept, Paragraph Subsection
graphing, Paragraph
intercept
horizontal, Paragraph
vertical, Paragraph
\(x\), Paragraph
\(y\), Paragraph
Intercepts
finding, Example
intersection, Definition
Interval notation, Definition
Inverse
additive, Paragraph
multiplicative, Paragraph
Inverse property
of addition, Paragraph
of multiplication, Paragraph
leading coefficient
of a polynomial, Definition
leading term
of a polynomial, Definition
Less-than symbol, Paragraph
Less-than-or-equal-to symbol, Paragraph
Like radicals, Item
Like terms, Paragraph
Linear equations, Definition
intercepts used for graphing, Subsection
solving, Subsection Process
with fractions, Paragraph
with infinitely many solutions, Example
with no solution, Example
Linear equations in one variable, Definition
Linear equations in two variables, Definition
graphing, Paragraph
Linear expression, Paragraph
Linear inequalities, Definition
solving, Subsection Process
Linear inequalities in one variable, Paragraph Definition
linear polynomial, Item
Linear system of equations, Definition
Lines
slope of, Definition
Mathematical models, Section
maximum, Paragraph
minimum, Paragraph
Mixture problems, Example
Modeling, Section
monomial, Item
Multiplication
associative property of, List
commutative property of, List
identity property of, Paragraph
inverse property of, Paragraph
Multiplication property
negative, Fact
Multiplication property of equality, Fact
Multiplicative identity, Paragraph
Multiplicative inverse, Paragraph
Negation property of equality, Paragraph
Negative multiplication property of inequality, Fact
Negative reciprocals, Fact
Negative signs and parentheses, Paragraph
Negative slope, Item
Not-equal-to symbol, Paragraph
\(n\)th root, Definition
\(n\)th radical, Definition
\(n\)th root, Definition Definition
Opposite, Paragraph
or, Paragraph
order of magnitude, Definition
Ordered pair, Section Definition
as solution of equation, Paragraph
as solution of linear system, Definition
Origin, Definition
parabola
axis of symmetry, Paragraph
horizontal intercept, Paragraph
opening up or down, Fact
vertex, Paragraph
vertical intercept, Paragraph
Parallel lines, Fact
and slope, Fact
Percent
applications, Subsection
as a decimal, Paragraph
perfect square trinomial, Paragraph
perfect squares, Paragraph
perimeter, Paragraphs
Perpendicular lines, Fact
and slope, Fact
Plotting points, Paragraph
Point-slope form, Definition
Points
plotting, Paragraph
polynomial, Definition
addition and subtraction, Subsection
coefficients, Definition
constant, Item
constant term, Definition
cubic, Item
degree, Definition
divided by a monomial, Subsection
leading coefficient, Definition
leading term, Definition
linear, Item
prime, Example
quadratic, Item
quartic, Paragraph
quintic, Paragraph
terms of, Definition
Positive slope, Item
power, Paragraph
prime polynomial, Example
Problem solving
with substitution method, Subsection
product of a sum and its conjugate, Fact
properties
square root property, Fact
zero product property, Fact
Proportions, Paragraph
applications of, Example
Pythagorean theorem, Theorem
Quadrant, Definition
quadratic, Paragraph
equation, Definition
equation in standard form, Definition
vertex, Fact
quadratic function
factored form, Fact
forms, Paragraph
vertex form, Fact
quadratic polynomial, Item
quartic polynomial, Paragraph
quintic polynomial, Paragraph
Radical, Definition Definition
radical, Definition
radical equation, Definition
Radical symbol, Definition Definition
Radicals
like, Item
radicand, Definition Definition
range, Definition
Rate, Paragraph
Rate of change, Subsection Definition
rational equation, Definition
rational function, Definition
rationalizing the denominator, Subsection
Real numbers
ordering, Checkpoint
negative, Fact
Rectangular coordinate system, Paragraph
finding coordinates of points, Section
Relationship
constant, Paragraph
Rise over run, Remark
root, Definition
roots of a function, Paragraph
Satisfy an equation, Paragraph
Satisfy an inequality, Paragraph
scientific notation, Definition
Set
empty, Warning
Set notation, Paragraph
Set-builder notation, Definition
Simplifying algebraic expressions, Example Checkpoint
Slope, Definition
and parallel lines, Fact
and perpendicular lines, Fact
as rate of change, Definition
definition, Definition
formula, Example
given intercepts, Fact
negative, Item
of a line, Definition
positive, Item
triangle, Example
undefined, Fact
zero, Item
Slope-intercept form, Definition
graphing lines in, Figure
Solution mixture problems, Example
Solution set
of equation, Paragraph
of inequality, Example
Solution(s)
of an inequality, Definition
of equations, Definition
of equations in two variables, Section
of system of linear equations, Definition
Solving
linear equations
multistep, Process
linear inequalities
multistep, Process
solving
absolute value equations
with one absolute value, Fact
with two absolute values, Fact
compound inequalities
three-part, Subsection
with "or", Subsection
inequalities
graphically, Subsection
quadratic equations
by completing the square, Subsection Process
by factoring, Process
factoring, Subsection
quadratic formula, Fact
using the square root property, Subsection
radical equations, Process
rational equations, Subsection Process
Solving an equation, Paragraph
Solving an inequality, Paragraph
Square root, Definition
square root, Definition
square root property, Fact
squaring a binomial, Subsection Fact
Standard form, Definition
standard form of a quadratic equation, Definition
problem solving with, Example Subsection Example
Substitution of number for variable, Example
Subtraction
translating phrases, Paragraph
Subtraction property of equality, Fact
Symbol
radical, Definition Definition
Systems of linear equations, Definition
applications, Example Checkpoint Example Subsection Example Example Example Example
solved by elimination, Subsection Process
solved by graphing, Subsection
with infinitely many solutions, Subsection Example Example
with no solution, Subsection Example Example
Systems of two linear equations
number of solutions, List
Variable, Paragraph
isolating, Paragraph
solving for in a formula, Paragraph
vertex form of a quadratic function, Fact
vertical asymptote, Remark
Vertical line, Example
slope of, Fact
vertical line test, Fact
vertical-intercept, Paragraph
volume, Paragraph
cylinder, Paragraphs
prism, Paragraphs
Word problems
strategy for solving, Section
\(x\)-intercept, Paragraph
\(x\)-axis, Definition
\(x\)-coordinate, Definition
\(x\)-intercept, Subsection
\(y\)-intercept, Paragraph
\(y\)-axis, Definition
\(y\)-coordinate, Definition
\(y\)-intercept, Paragraph Subsection
