Algabria 2 Vocab
Exsperimental probability of evnt
P(event) = number of times that an event occurs over number of trials
Factoring
rewriting an expression as the product of its factors
center
middle
Monomial
A number, a variable, or a product of a number and one or more variables
Trinomial
A polynomial with 3 terms
Matrix
A rectangular array of numbers. You usually display the array of numbers within the columns in the array.
function
A relation in which each element of the domain corresponds with exactly the one element of the range
combination
A selection of numbers or objects in which order does not matter
Domain
A set of inputs, also called x coridinants, of the orderd pairs
diffrence of two squares
A squred - b squred
Equation
A statement where the two expressions are equal
How to factor the diffrence of two squres
A sured - b squred = (a + b)(a -b)
Variable
A symbol, usually a letter, that represents one or more numbers Exsanmples: n, x
row operations
A system used to solve a matrix
Constant term
A term with no variables
zero of a function
A value of x where f (x) = 0
data point
A value that originates in a worksheet cell and that is represented in a chart by a data marker
box and whisker plot
A way to display dat that uses -quartertiles to bound the center box and -the minimum and maxim values that form the whiskers
Distrubutive Property for subtraction
A(b-c) = ab-ac
Asscociate Property
Addition: (a + b) + c = a + (b + c) Multiplication: (ab)c = a(bc)
Communitive property
Addition: A + b = b + a Subtraction: ab = ba
Property of clousure
Addition: a + b is a real number Subtraction: ab is a real number
consecutive
All in a row or pattern, 123 ect.
permutation
An arrangement of items in a particular order.
literal equation
An eqaion that uses two different letters as variables
Outlier
An outlier is a value that is substantially different from the rest of the data in a set. If the data is in one variable, outliers can occur at the ends. They can be misleading because they affect measures of central tendency.
And and Or
And means that a solution is always true Or means that a solution makes either inequality true,
n factorial
N! = n(n-1) * ... * 3 * 2 * 1. Zero factorial is 0! = 1.
Complex conjagations
Number pairs of the form a + bi and a - bi
irrational numbers
Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.
Unnatural numbers
Odd numbers basiclly
Open and closed circles
Open circles stand for greater then Closed stand for less then or equal to
Inverse operations
Operations that undo each other
Zero Product Property
if ab=0, then a=0 or b=0
vertex of a parabola
(H, k) the intersection of the parabola and it's axsis summery
standard form of a circle
(x-h)2 + (y-k)2 = r2
Opposite of an Opposite
-(-a) = a [If a is a positive number, then the answer will be positive as well]
Opposite of a Sum Property
-(a+b)=(-a)+(-b)
Opposite of a Difference
-(a-b) = -a + b = a -b
Opposite of a product
-(ab) = -a x b = a x (-b)
multiplication by -1
-1 x a = -a
Opposite or additive inverse
-a Examples: 12 + (-12) = 0 where -12 is -a -7 + 7 = 0 where -7 is -a
Multiplication by 0
0 x a = 0
Reciprocal or multiplication inverse
1/a Examples: 8(1/8 = 1 where 1/8 is 1/a -5(-1/5) = 1 where -1/5 is 1/a
distibutive property for subtraction
A (b - c) = ab - ac
Definition of Division
A / b = a over b = a . 1 over b, b is not equal to o
Bimodal
A bimodal set has two modes. If a data set has more then two modes, then the modes are probably not statistically useful. If no value occurs more frequently then any other, then there is no mode.
Equally likely sample space
A combination of equally likely events in a set
greatest common factor (GCF)
A common factor of the terms in the exspression. It is the common factor with the greatest coefficent and the greatest exsponent. You can factor any exspression that has a GCF not equal to 1.
positive correlation
A correlation where as one variable increases, the other also increases, or as one decreases so does the other. Both variables move in the same direction.
Translation
A function that moves an object a certain distance
linear function
A function whose graph is a line
Scatter plot
A graph that relates two sets of detail by plotting the data as ordered pairs.
Axises of summery
A line that divides the parabola line into two mirror images. The equation of the axis summery is x = h
Numeric exspression
A mathematical phrase that contains numbers and open sybols Exsamples: 3 + 5 (8-2 + 5)
Algebraic exspression
A mathematical phrase that contains one or more variables Exsamples: 3n + 5 (8x-2 + 5n)
simulation
A model of an event
function rule
A n eqasion that represnts an output value in terms of an input value
Percentile
A number from 0 to 100 that you can associate x value from a data set. it shows the percent of the data that are less then or equal to x. If x is at the 63erd percentile, then 63% of the data are less then or equal to x.
principal root
A number that has a positive and a negative root
Imiginary number
Any number in the form of A + bi where a and b are real numbers and b does not equal 0
Matrix element
Any number within a matrix
standerd form of a linear equation
Ax + By = C where A, B and C are real numbers and A and B are not both 0.
Complex number
Coplex numbers in the form of a + bi where a and b are real numbers and b is not = to 0 If b = 0 the number a + bi is a real number If a = 0 and b does not equal zero the number a + bi is a pure imiginary number
Transformation
Each function in a family
Quadratic function, which you can write in the form of f(x) = ax to the second power + bx + c
F(x) = ax to the second power + bx + c
Key concepts box: The parent quadratic function
F(x) = x to the second power is the parent quadric function. It's graph shows is the parabola shown in the box see photos The axis of symmetry is x = 0. The vertex is (0,0)
dependent variable
F(x); it represents the output of the function. It is called the dependent variable because its value depend on the input value.
Median
For a data set listed in order, the middle value for an odd number of data values; the mean of the two middle values for an even number of data values Exsample: for 1, 2, 3, 4, 5, 5, 9, the middle two values are 3 and 4. The median is their mean 3 + 4 over 2 = 3.5
nth root
Given the sequence of equasions a(n) = b,a is the nth root of b
Like terms
Have the same variables raised to the same powers
theorectical probability
If a sample space has n equally likely outcome and an event A occurs in m of these outcomes, then the theoretical probability of event A is P(A) = m over n.
Measure Of central tendency
Indicates the middle of a data set. The mean median and mode are the most common uses of central tendency
verticle line test
It sates that if a vericle line passed es through more than one point of the graph of a relation, then the relation is not a function
Slope of a line
Positive slope, line rises left to right. Negative slope, line falls from left to right Zero slope, horizontal line. Unidentified slope, vertical line.
Variable Quantity
Quantities whose values change or vary
Constant
Quantities whose values do not change
correlation coefficient
R; indicates the strength of a correlation.
Slope
Ratio of horizontal vs vertical change or rise over run in a graph
verticle compression
Ruduces all y values of a function to the same function between 0 and 1.
Concept Summery: Writing Equations of Lines
Slope Intercept form: y = mx + b Use this form when you know the slope and y intercept. Point Slope Form: y - y1 = m(x - x1) Use this form when you know the slope and a point, or points. Standard Form: Ax + By = C A, B and C are real numbers. A and B cannot both be zero.
mean
Sum of data values over number of data values Example: 1 + 2+ 3 + 3 + 4 + 5 + 5 + 9 over 8 = 4
imaginary unit
The complex number whose squre is -1. So i squred = -1 and i = the saure route of -1
Range of a set of data
The difference between the greatest value to the least value. If you order the data from least value to greatest value, the. The median divides the data into two parts. The median of each part divides rhe data further and tou have four parts in all.
interquartile range
The difference between the third and first quantities
Discrimanent
The discriminant of a quadratic equasion is in the form of ax squred + bx + c = 0 is the value of the exspression b squred - 4ac
perimeter
The distance around a figure
Radius
The distance from the center of a circle to any point on the circle
linear equation
The equation that represents a linear function
Parabola
The graph of a quaderatic function
Parabla
The graph of a quadratic function which you can write in the form of f(x) = ax squred + bx + c where a is not = 0
Fundimental Counting Principle
The method of using multiplication to count
Mode
The most frequently occurring values Exsample: two modes: in 1, 2, 3, 4, 5, 5, 9, both 3 and 5 occerd twice
Index
The number that gives the degree of the root
Radicand
The number under the radical sign
Complex number plaine
The point (a,b) represents the complex number a + bi. To graph a complex number, locate the rewal part on the horizontial axsis and the imaginary part of the y axsis
Reflection
The process by which a graph of a function is flipped across the line, such as the x or y axis. Each point on the graph of the reflected function is the same distance from the line of reflection as it's corresponding point on the graph of the original function.
experimental probability
The ratio of the number of times an event occurs to the total number of trials, or times that the activity is performed.
Sample space
The set of all possible outcomes to an experiment or activity
Range
The set of outputs, also called y coridinanents of the orderd pairs
parent function
The simplest form of a set of functions that form a family.
Slope
The slope of a non-vertical line through set of points (x1, y1) and (x2, y2) is the tratio of the vertical change to the corissponding horizontal change.
parelell lines
The slope of parallel lines are equal.
perpindicular lines
The slope of these lines are negative reciprocals of each other.
Correlation
The strenth of a relationship between two points.
Cube root
The third root of a number
quantities
The values that separate a set of data.
verticle stretch
The vertice stretch is the thing that manipulates all y values of a function by the same factor greater than 1.
fuction notation
The way to write a function rule
minimum value
The y codinate of the vertewx If a < 0, the parabola opens downwards
maximum value
The y coordinate of the vertex.
maximum value
The y cordinate of the vertex
Minimum value
The y cordinate of the vertex.
Evaluate
To evaluate an expression, substitute a number for each variable in the equation. Then simplify using order of operations.
Solution of an equasion
To find the solution of an equasion, isolate the variables on each side of the equasion using inverse operations
compound inequality
Two inequalities with the words and and or To solve a compound inequality, containing and, find all values of the inequality that make both inequalities true.
Theoretical Probability
What should occur or what we expect to happen in an experiment
Equally likely outcomes
When each outcome in a sample space has the same chance of occurring
combined variation
When one quantity varies directly and/or inversely as two or more other quantities
X >/= 4
X is greater than or equal to 4 To graph: draw a closed circle above the 4 on the number line and then draw an arrow to the right.
X > 4
X is greater then 4 To graph: place a open circle above the 4 on a number line a draw an arrow going to the right
X < 4
X is less than 4 To graph: draw a open circle above the 4 on a number line and then draw a line going to the left.
X </= 4
X is less than or equal to 4 To graph: draw a closed circle above the 4 on a number line then draw a line going to the left.
How to form a perfect square trinomial from x squred by adding b/2 squred.
X squred + bx + (b/2) squred = (x + b/2) squred
independent variable
X; it represents the input of the function
The equation of a line through point (x1, y1) with the slope as m
Y - y1 = m(x - x1)
direct variation
Y = kx or y over x = k where k is not equal to 0
slope intercept
Y = mx + b where m is the slope of a line and (0, b) is the y intercept
Sample Space (Probability)
list of all possible outcomes
diagram
a drawing intended to explain how something works
cubic
a polynomial with a degree of 3
Quintic
a polynomial with a degree of 5
Relation
a set of pairs of input and output values
perfect square trinomial
a trinomial that is the square of a binomial For exsample, x squred + 10x + 25 = (x + 5) squred
simulation
a way to model random events
distibutive property
a(b+c)=ab+ac
Definition of Subtraction
a-b=a+(-b)
Inverse Variation
an equation of the form y = k/x, where k is not equal to zero
Identity
an equation that is true for every value of the variable
Term
an expression that is a number, a variable, or the product of a number and one or more variables
Negative correlation
as one variable increases, the other decreases
Natural Numbers
counting numbers
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
absolute value of a complex number
distance from the origin on the complex number plane Or I a + b I = the square route of a squared + b squared
Bimodal
distributions with two modes
Vertex form
f(x) = a(x-h)^2 + k
plotting
finding the data point for an ordered pair
Linear
straight line
Coefficent
the numerical factor of a term
complete the square
the process of adding a term to a quadratic expression to make it a perfect square trinomial
Constant of a variation
the ratio of all output-input pairs equals the constant k (except for (0, 0) )
parent graph
the simplest of the graphs in a family of graphs
Binomial
the sum of two monomials
line of best fit
the trend line that gives the most accurate model of related data
x-intercept
the x-coordinate of a point where a graph crosses the x-axis
y-intercept
the y-coordinate of a point where a graph crosses the y-axis
Integers
whole numbers and their opposites
Quadratic Formula
x = -b ± √(b² - 4ac)/2a
joint variation
y varies jointly as x and z if there is some nonzero constant k such that y=kxz