Algebra II Unit 1
x- coordinate of vertex
-b/2a
Additive Identity Element
0 is the additive identity element because for every number a , a+0=0+a=a
Multiplicative Identity Element
1 is the multiplicative identity element because for every number a, a*1=1*a=a
discriminant = 0
1 real solution
discriminant > 0
2 real solutions
relation
A ___ is any set of ordered pairs.
function
A relation in which each domain element is paired with exactly one range element is a ___.
inverse
An ___ is a relation found by interchanging the domain and range values in each ordered pair of a relation.
natural numbers closure
It is closed under addition and multiplication but not closed under subtraction or division.
Rational and real number closure
It is closed under addition and subtraction, multiplication, and division, with the exception of division by 0 which is not defined.
range
The ___ is the set of second coordinates of each ordered pair in a relation.
domain
The set of first coordinates of each ordered pair in a relation is the ___.
term
a constant, variable, or the product of a constant and variables
graph
a diagram showing the relations among numbers
asymptote
a line that a graph gets closer to as the value of a variable gets extremely large or extremely small.
polynomial
a mathematical expression consisting of constants and variables, combined with the operations of addition and multiplication
monomial
a polynomial with one term
trinomial
a polynomial with three terms
binomial
a polynomial with two terms
exponential equation
an equation in the form y=ab^x.
linear equation
an equation in which each term is either a constant or the product of a constant and a single variable
quadratic equation
an equation of the form ax²+bx+c=y where a, b, and c are real numbers and a ≠ 0
radical equation
an equation that contains a variable within a radical expression
rational equation
an equation that contains at least one rational expression
radical expression
an expression that includes a radical.
linear inequality
an inequality in which each term is either a constant or the product of a constant and a single variable
quadratic inequality
an inequality of the form ax²+bx+c<y where a, b, and c are real numbers and a ≠ 0 , or any similar form with >, ≤, or ≥
Trichotomy Property
for any numbers a = b, either a < b, or a = b, or a > b
Commutative Property of Multiplication
for any numbers a and b, a*b=b*a
Commutative Property of Addition
for any numbers a and b, a+b=b+a
Symmetric Property of Equality
for any numbers a and b, if a = b, then b = a
Associative Property of Multiplication
for any numbers a, b, and c, a*(b*c)=(a*b)*c
Distributive Property of Multiplication over Addition
for any numbers a, b, and c, a*(b*c)=(a*b)+(a*c)
Associative Property of Addition
for any numbers a, b, and c, a+(b+c)=(a+b)+c
Transitive Property of Equality
for any numbers a, b, and c, if a = b and b = c, then a = c
Multiplicative Inverse Property
for every number a except 0, there is a number a-¹=1/a, such that a*(a-¹)=(a-¹)*a=1
Reflexive Property of Equality
for every number a, a = a
Additive Inverse Property
for every number a, there is a number −a, such that a+(-a)=(-a)+a=0
Zero Product Property
if ab = 0, then a = 0 or b = 0
Substitution Property of Equality
if x = y, then y can be substituted for x in any expression
integers closure
is closed under addition, subtraction, and multiplication but not closed under division
Irrational numbers closure
is not closed under any of these operations
∈
member of
discriminant < 0
no real solutions
∉
not a member of
rational numbers
numbers of the form a 0 and designated with Q
integers
numbers {0, +1, −1, +2, −2, . . .} and designated with Z
whole numbers
numbers {0, 1, 2, 3, . . .}
natural numbers
numbers {1, 2, 3, 4, . . .} and designated with N
irrational numbers
real numbers which cannot be written as the ratio of two integers; designated with Q⌒
⊂; { }
subset of; set notation
discriminant
the expression, b²-4ac, which tells the nature of the roots of a quadratic equation
quadratic formula
the formula, [-b±√(b²-4ac)]/2a, used to find the solutions to a quadratic equation
closure
the property of an operation and a set that the performance of the operation on members of the set always yields a member of the set
rational expression
the quotient of two polynomials
real numbers
the rational numbers together with the irrational numbers; designated with R
∪
union
