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Common Core Algebra Regents Vocabulary
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Gravity
Get ready for June 3rd!
Key Concepts:
Terms in this set (120)
absolute value
|n| is the distance from 0 to a number n on a number line. Ex |-3| = 3 and |5| = 5
absolute value function
A function containing the |x|. It is shaped like the letter v
What does the graph of an Absolute Value Function Look Like
V or upside down V
What does a Quadratic Graph Look like
PARABOLA - The U shaped graph with a point(vertex) at the bottom or top.
What you do you know about the slopes of Parallel Lines
They are the same.
What do you know about the slopes of perpendicular lines
They are negative reciprocals. (Flip and change the sign)
Axis of Symmetry
x = -b / 2a; Axis of symmetry is ALWAYS an equation x = ____
How do you factor the difference of two squares a^2 - b^2
(a - b)(a+b)
Definition of "to factor"
To break a number or expression down into its multiplicative parts. For example you factor x^2 + 5x + 6 as (x+2)(x+3)
Definition of "to solve"
To find the value of a variable that makes an equation true. For example you solve x - 2 = 4 by finding x = 6
What is the Line of Best Fit or Trend Line
It is the best line that can be drawn on a scatter plot that accurately represents the trend of the data.
What is a residual and when is a residual plot an indicator that you have a good model.
residual = actual - predicted; A residual plot indicates that a model is good when there is no pattern
What is the MODE in data
Most frequent number
What is the mean in data
It is the average
What is the median in data
Is is the middle number or average of the two middle numbers AFTER THEY ARE ARRANGED IN ORDER
Explain how to use the calculator to find the 5 numbers for a Box and Whisker plot
Hit STAT, then Edit and type in the values into L1. Once done hit STAT again -> to CALC and click on 1 Var Stats then scroll down to see the five number summary
RANGE of a data set
Maximum # - Minimum #
equation of a vertical line
the equation of a vertical line is always x = a number such as x = -5
equation of a horizontal line
the equation of a vertical line is always y = a number such as y = -5
product
the result of multiplication
sum
the result of addition
slope-intercept form of a line
y = mx + b; m is the slope and b is the y-intercept
vertex form of a quadratic equation
y=a(x-h)^2 + k ; (h,k) is the vertex
standard form of a quadratic equation
y = ax^2 + bx + c ; a tells you whether the parabola opens up or down
algebraic solution
This means you need to solve the problem using variables and equations. Guess and check, graphing calculators, or other solution methods will earn partial credit
expresion
A mathematical statement with variables and constants but which does not contain any relation symbol (<,>,=,...)
equation
A mathematical statement with variables and constants which contains an equal sign
associative property
Sum or product of terms has the same value, regardless of how the terms are grouped. Example: 2x + (3 + y) = (2x + 3) + y
base
A number that is raised to a power
binomial
Polynomial with two terms Ex. (x + 4)
bivariate data
Data involving two seperate things being measured (Ex. height and age of a group of students)
box and whisker plot
closure
An operation is said to be closed if the output is the same type as the input. Example: Positive numbers are closed under addition because when you add two positive numbers the result is a positive number
coefficient
The numerical factor of a term in a polynomial. Example: 14 is the coefficient in the term 14x
greatest common factor (GCF)
The greatest number, polynomial, or quantity that divides two or more numbers or algebraic expressions evenly
commutative property
A property of real numbers that states that the sum or product of two terms is unaffected by the order in which the terms are added or multiplied; i.e., the sum or product remains the same. . Ex: 2x + y = y + 2x
coordinate pair
(x, y)
correlation
Measures how strong the relationship between two variables is
correlation coefficient
"r value"; between -1 and 1. The further away from zero, the stronger the relationship between the two variables are
cummulative frequency table
A table that shows how often each item, number, or range of numbers occurs in a set of data. This table displays the total number of scores that fall into each of several cumulative intervals. The cumulative intervals are created by adding the preceding tallies (of lower scores) to the new tallies for each interval.
degree of a polynomial
The highest exponent value in the polynomial.
difference of perfect squares
A binomial of the form a^2 - b^2 which can be factored into (a - b)(a + b)
distributive property
A property of real numbers that states that the product of a number and the sum or difference of two numbers is the same as the sum or difference of their products. Example: 2( 3 + x) = 2(3) + 2(x)
exponent
A number that tells how many times the base should be multiplied by itself
expontial decay
An amount is multiplied by a number less than one every period time. Represented by y = a(b^x) where a is the initial value and b is the rate
exponential function
An function with a variable in the exponent. Has a multiplicative rate of change
exponential growth
An amount is multiplied by a number greater than one every period of time. Represented by y = a(x^x) where a is the initial value and b is the rate
factor (verb)
Break an expression into its multiplicative parts. "unmultiply"
five number summary
Minimum, 1st quartile, median, 3rd quartile, and maximum
frequency table
A table that shows how often each item, number, or range of numbers occurs in a data set.
function
Each input can only have one ouput! Formally: A rule that assigns to each number x in the function's domain a unique number f( )x .
histogram
A type of graph for 1 variable quantitative data. The horizontal axis is a number line that displays the data in equal intervals. The frequency of each bar is shown on the vertical axis.
hypotenuse
The side of a right triangle opposite the right angle; the longest side of a right triangle.
identities
equations that are true for all values of the variable they contain. Example x + 2 = 2 + x
inequality
A mathematical statement containing one of the symbols <, >, ≤,≥,≠to indicate the relationship between two quantities.
integers
{...-4, -3, -2, -1, 0, 1, 2, 3, 4, ... }
leading coefficient
"The coefficient of the first term of a polynomial when the polynomial is in standard form. 5 is the leading coefficient of 5x^2- 9x + 7
Pythagorean Triple
Whole numbers that satisfy the pythagorean theorem
simplest radical form
Use factor tree to find the most simplified version of a square root
line of best fit
A line used to approximate and generalize the linear relationship between the independent and dependent variables for a set of data.
literal equation
An equation that contains more than one variable. Ex: 2a + 3y = c
mean
Another name for average. Add all the numbers and divide by how many there are (or get your calculator to do it for you!)
measure of central tendancy
"A summary statistic that indicates the typical value or center of an organized data set. The three most common measures of central tendency are the mean, an organized data set. The three most common measures of central tendency are the mean,
median, and mode. "
...
median
Middle value in a data set
mode
The most frequent number in a data set
monomial
A polynomial with one term (it has a coefficient and a variable)
mutliplication property of zero
For every number a, 0 • a = 0 and a • 0 = 0.
parabola
U shape made by a quadratic function
parallel lines
Same slope different y intercept
perimeter
Add up all the sides to find the length around a shape
polynomial
A sum of monomials (2 or more terms)
proportional
Two variables are proportional if they maintain a constant rate of change and include the point (0,0)
quadratic function
A function with an x^2 term
linear function
A function with a constant rate of change; often in the form y = mx + b
quantitative
Descriptions using numerical measures such as quantity, height, or age.
qualitiative
Descriptions using word categories such as favorite color, type of eye color, or name
domain
All possible input values (x values)
range
All possible output values (y values)
right triangle
Go to your formula sheet and use the pythagorean theorem
real numbers
All the numbers on the number line
roots of an equation
A solution to an equation of the form f(x) = 0; find on a graph by looking at the y-intercepts OR by using factoring to solve OR by using the quadratic formula
scatter plot
Displays the relationship between two variables. DO NOT connect the lines
slope
Constant rate of change: change in y over change in x
solution set
All solutions written in curley brackets Ex if x = 0 or x = -3 the solution set is x = {0,-3}
system of equations/inequalities
(x,y) that satisfy all equations or inequalities
substitution
Method for solving systems of equations. Get a variable by itself and plug it into the other equation
elimination
Method for solving a system of equations. Add the equations together to get a variable to cancel out.
trinomial
A polynomial with three terms
univariate
A data set involving one variable
vertex
The maximum or minimum point of a parabola
recursive function
Function that goes step by step. Start with f(1) then find f(2)...
axis of symmetry
x = -b/2a ; The x value in a vertex of a parabola
zero product property
If two terms multiplied equals zero, one of the terms equals zero; IE if ab=0 either a=0 or b=0
Quartile
Breaks a data set into 4 equal bins each with 25%
Arithmetic sequence
Sequence where the rate of change is additive; Look on your formula sheet for the general form
Geometric sequence
Sequence where the rate of change is multiplicative; Look on your formula sheet for the general form
Factored form
y = (x - r)(x - s); shows the roots of a parabola
Standard form of a quadratic
y = ax^2 + bx + c; shows the y intercept of a parabola
Slope intercept form of a line
y = mx + b where m is the slope and b is the y intercept
Turning point
Another name for the vertex of a parabola
Factor completely
Make sure to look for GCF's to factor! Use slide divide bottoms up if the leading coefficient is still not equal to one after factoring out a GCF
Solution to a system of equations
Point(s) where two equations intersect
Solution to a system of inequalities
Shaded region where two inequalites intersect
Square root function
Function with a square root; use graphing calculator to visualize
Irrational numbers
Numbers that can't be written as a fraction
Vertical shift of a function
f(x) + k or f(x) - k
Horizontal Shift of a function
f(x - h) or f(x + h)
Vertical dilation (stretch) of a function
a f(x)
Residual
Actual value - predicted value; A linear model is a good fit if the graph of these is random
Zeros of a graph
The x intercepts or solutions
Restriction on the domain of a graph
These are the domain values that would make a function undefined. Ex f(x) = 1/x x would be restricted so that x can't be equal to zero
Causal Relationship
Does one variable CAUSE the other variable. Remember, correlation doesn't mean causation!
Interquartile range
The difference between Q1 and Q3
average rate of change
Change in y over change in x; make a table using your graphing calculator to help!
Cubic
A function with x raised to a power of 3
point-slope form of a line
y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the graph
Dot Plot
Number line with a dot for each data point above it
Where can I find the absolute value sign on my calculator?
Press the MATH button, scroll right to NUM and look for abs()
Where can I find cube roots on my calculator?
Press the MATH button and scroll down.
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