perpendicular lines Perpendicular lines
are two lines that intersect to form a right
(90°) angle. (Section 3.3)
plot To plot an ordered pair is to locate
it on a rectangular coordinate system.
(Section 3.1)
point-slope form A linear equation is writ-
ten in point-slope form if it is in the form
, where mis the slope
and is a point on the line. (Section 3.4)
polynomial A polynomial is a term or a
finite sum of terms in which all coefficients
are real, all variables have whole number ex-
ponents, and no variables appear in denomi-
nators. (Section 5.4)
polynomial in x A polynomial whose only
variable is xis called a polynomial in x.
(Section 5.4)
positive number A positive number is
located to the right of 0 on a number line.
(Section 1.4)
prime factor A prime factor of a number
is a factor greater than 1 whose only factors
are 1 and itself. For example, the prime fac-
tors of 12 are. (Section 1.1)
prime number A natural number greater
than 1 is prime if it has only 1 and itself as
factors. (Section 1.1)
prime polynomial A prime polynomial is
a polynomial that cannot be factored into
factors having only integer coefficients.
(Section 6.2)
principal root (principal nth root) For
even indexes, the symbols , ,
, , are used for nonnegative
roots, which are called principal roots. (Sec-
tion 8.1)
product The answer to a multiplication
problem is called the product. (Section 1.1)
product of the sum and difference of two
terms The product of the sum and differ-
ence of two terms is the difference of the
squares of the terms, or
. (Section 5.6)
proportion A proportion is a statement
that two ratios are equal. (Section 2.6)
proposed solution A value that appears as
an apparent solution after a rational or radi-
cal equation has been solved according to
standard methods is called a proposed solu-
tion for the original equation. It may or may
not to be an actual solution and must be
checked. (Sections 7.7, 8.6)
pure imaginary number If and
in the complex number the
complex number is called a pure imaginary
number. (Section 9.4)
Pythagorean theorem The Pythagorean
theorem states that the square of the length
of the hypotenuse of a right triangle equals
the sum of the squares of the lengths of the
two legs. (Section 6.6)quadrant A quadrant is one of the four
regions in the plane determined by the axes
in a rectangular coordinate system. (Sec-
tion 3.1)
quadratic equation A quadratic equation
is an equation that can be written in the form
, where a,b, and care
real numbers, with. (Sections 6.5, 9.1)
quadratic formula The quadratic formula
is a general formula used to solve a quadratic
equation of the formwhere It is
(Section 9.3)
quadratic function A function defined by
an equation of the form
for real numbers a,b, and c, with
, is a quadratic function. (Section 9.5)
quotient The answer to a division problem
is called the quotient. (Section 1.1)radical An expression consisting of a rad-
ical symbol, root index, and radicand is
called a radical. (Section 8.1)
radical equation A radical equation is an
equation with a variable in at least one radi-
cand. (Section 8.6)
radical expression A radical expression is
an algebraic expression that contains radi-
cals. (Section 8.1)
radical symbol The symbol is called
a radical symbol. (Section 8.1)
radicand The number or expression under
a radical symbol is called the radicand. (Sec-
tion 8.1)
range The set of all second components
(y-values) in the ordered pairs of a relation
is called the range. (Section 3.6)
ratio A ratio is a comparison of two quan-
tities using a quotient. (Section 2.6)
rational expression The quotient of two
polynomials with denominator not 0 is
called a rational expression. (Section 7.1)
rationalizing the denominator The pro-
cess of rewriting a radical expression so
that the denominator contains no radicals
is called rationalizing the denominator.
(Section 8.4)rational numbers Rational numbers can
be written as the quotient of two integers,
with denominator not 0. (Section 1.4)
real numbers Real numbers include all
numbers that can be represented by points
on the number line—that is, all rational and
irrational numbers. (Section 1.4)
real part The real part of a complex num-
ber is a. (Section 9.4)
reciprocal (Seemultiplicative inverse.)
rectangular (Cartesian) coordinate sys-
tem Thex-axis and y-axis placed at a right
angle at their zero points form a rectangular
coordinate system. It is also called the Carte-
sian coordinate system. (Section 3.1)
relation A relation is a set of ordered pairs.
(Section 3.6)
right angle A right angle measures 90°.
(Section 2.4)
rise Rise refers to the vertical change
between two points on a line—that is, the
change in y-values. (Section 3.3)
run Run refers to the horizontal change
between two points on a line—that is, the
change in x-values. (Section 3.3)scatter diagram A scatter diagram is a
graph of ordered pairs of data. (Section 3.1)
scientific notation A number is written in
scientific notation when it is expressed in
the form , where and
nis an integer. (Section 5.3)
set A set is a collection of objects. (Sec-
tion 1.3, Appendix)
set-builder notation The special symbol-
ism has a certain property is called
set-builder notation. It is used to describe a
set of numbers without actually having to list
all of the elements. (Section 1.4)
signed numbers Signed numbers are
numbers that can be written with a positive
or negative sign. (Section 1.4)
simplified radical A simplified radical
meets three conditions:- The radicand has no factor (except 1) that
is a perfect square (if the radical is a
square root), a perfect cube (if the radical
is a cube root), and so on. - The radicand has no fractions.
- No denominator contains a radical.
(Section 8.4)
slope The ratio of the change in yto the
change in xfor any two points on a line is
called the slope of the line. (Section 3.3)
5 x|x 6a* 10 n 1 ...|a| 610S
a+bi2R
aZ 0bx+c,ƒ 1 x 2 =ax^2 +x=- b 2 b^2 - 4 ac
2 a
aZ0..
ax^2 +bx+c=0,aZ 0ax^2 +bx+c= 0Q
bZ 0 a+bi,
a= 0x^2 - y^2
1 x+y 21 x-y 2 =26 Á 2 n
2 242 # 2 # 3
1 x 1 ,y 12y-y 1 =m 1 x-x 12
G-4 Glossary
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