Order of Operations
Parenthesis
Exponents
Multiplication/Division
Addition/Subtraction
Equation
a mathematical sentence where the two sides have the same value
Similar terms
two terms in an equation with the same variable or no variable
Ordered Pairs
a coordinate point on a quadrant of the graph or grid; two parts of every one is the domain and range; (x,y)
Function
set of ordered pairs (relation) in which each element of the domain is paired with exactly one element in the range
Vertical Line Test
process of identifying functions by observing if a vertical line can pass through only one point on the graph at most (if a vertical line passes through two or more points on the graph, then the relation is not a function); visual way to determine if a cu
Linear Equation
an equation that represents a linear function (a function whose graph is a line) with no exponents
Quadratic Function
set of ordered pairs with the highest exponent to the second
Discriminant
Used to determine the number and type of solutions for any quadratic equation; part of the quadratic formula: ?b�?4ac
If it is > 0, 2 real solutions
If it is < 0, 2 imaginary solutions
If it is = 0, 1 real solution
Factoring Methods
GCF
Difference of Two Squares
Trinomials
Sum and Difference of Two Cubes
Grouping
Quadratic Formula
used to find the solution of a quadratic function
x = -b � ?b�?4ac � 2a
Monomial
an algebraic expression that is either a number, a variable, or the product of a number and one or more variables
Polynomial
a monomial or the sum of monomials, each of which is called a term
Sets of Numbers
set of real numbers divided into natural numbers, whole numbers, integers, rational numbers, and irrational numbers in the Number System (does not include set of imaginary numbers)
Evaluate
to find a solution by using the inverse operations to find the value of "x" that makes the equation true
Opposites
two integers on different sides of the number line that are the same distance away from zero
Quadrants
each of the four parts of a plane divided by two lines or planes at right angles
Function Notation
known as "f or x" or a "function of x"; the symbol f(x) replaces the y; f is the name of the function and is not multiplied by the x (letters other than f can be used to represent a function)
Slope of a Line
ratio of the vertical change of a line compared to the horizontal change of a line
Slope-Intercept Form
way of writing the equation of a line so that slope and y-intercept are immediately apparent; y = mx + b
Equation forms of quadratic
Standard Form
Vertex Form
Intercept Form
Axis of Symmetry
the line perpendicular to the parabola's directrix and passing through its focus and vertex
Square Roots/Radicals
an expression of the form ?s where s is a number or an expression; the symbol ? that tells us to find the square root of a number; a number that produces a specified quantity when multiplied by itself
Completing the Square
the process of adding a term to a quadratic expression of the form x� + bx to make it a perfect square trinomial
Binomial
an algebraic expression of the sum or the difference of two terms
Degree
the power of the exponent
Coefficient
the number of this power when a term is the product of a number and a power of a variable
Inequality
the relation between two expressions that are not equal, employing a sign such as ? (not equal to), < (less than), > (greater than), ? (less than or equal to), ? (greater than or equal to)
Reciprocal
Switching the numerator and the denominator of a number in the form of a fraction
Domain
set of all inputs, or x-coordinates, of the ordered pairs in a relation
Range
set of all outputs, or y-coordinates, of the ordered pairs in a relation
Intercepts
point where the curve crosses an axis (x-intercept = x-axis; y-intercept = y-axis)
Vertex
the one place that is the highest or lowest (depending on the graph) point (ordered pair) of the curve of the parabola
Parabola
the set of all points equidistant from a point called the focus and a line called the directrix; a symmetrical curve on the graph of a quadratic function y = ax� + bx + c
Minimum/Maximum
Maximum Value of a Quadratic Function= the y-coordinate of the vertex for y = ax� + bx + c when a<0
Minimum Value of a Quadratic Function= the y-coordinate of the vertex for y = ax� + bx + c when a>0
Imaginary Number
a number that is not real and comes from finding the square root of a negative number; i = ?-1
Complex Numbers
using imaginary numbers with real numbers
Trinomial
an algebraic expression consisting of three terms
Synthetic Division
a shorthand method used to divide a polynomial by a divisor of the form x ? k (linear factor)