Common Core Algebra Regents Vocabulary
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,
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
correlation coefficient
"r value"; between -1 and 1. The further away from zero, the stronger the relationship between the two variables are
Identify the domain {(4,10)(-1,7)(12,-4)(-1,2)(-6,5)}
(4,-1,12,-6)
How do you factor the difference of two squares a^2 - b^2 Ex 1: x² - 81 Ex 2: 9x² - 25 Ex 3: 36a⁴ - 25b² Ex 4: 16 - 4x²
(a - b)(a+b) Ex 1: (x - 9)(x + 9) Ex 2: (3x + 5)(3x - 5) Ex 3: (6a² - 5b)(6a²+5b) Ex 4: (4 - 2x)(4 + 2x)
coordinate pair
(x, y)
system of equations/inequalities
(x,y) that satisfy all equations or inequalities
Joy wants to buy strawberries and raspberries to bring to a party. Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. If she only has $10 to spend on berries, which inequality represents the situation where she buys x pounds of strawberries and y pounds of raspberries?
1.60x + 1.75y ≤ 10
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise at least $500 to cover the cost of renting costumes. The students can accept a maximum of 360 cans and bottles. Write a system of inequalities that can be used to represent this situation.
2x + 1.5y ≥ 500 x + y ≤ 360
Alicia purchased H half gallons of ice cream for $3.50 each and P packages of ice cream cones for $2.50 each. She purchased 14 items and spent $43. Write a system of equations that models this situation.
3.50H + 2.50P = 43 H + P = 14
absolute value function
A function containing the |x|. It is shaped like the letter v
linear function
A function with a constant rate of change; often in the form y = mx + b
quadratic function
A function with an x^2 term
Cubic
A function with x raised to a power of 3
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.
inequality
A mathematical statement containing one of the symbols <, >, ≤,≥,≠to indicate the relationship between two quantities.
expression
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
base
A number that is raised to a power
trinomial
A polynomial with three terms
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)
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
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
Residual
Actual value - predicted value; A linear model is a good fit if the graph of these is random
perimeter
Add up all the sides to find the length around a shape
domain
All possible input values (x values)
range
All possible output values (y values)
solution set
All solutions written in curley brackets Ex if x = 0 or x = -3 the solution set is x = {0,-3}
real numbers
All the numbers on the number line
exponential growth
An amount is multiplied by a number greater than one every period of time. Represented by y = a(b)^x where a is the initial value and b is the rate
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
literal equation
An equation that contains more than one variable. Ex: 2a + 3y = c
exponential function
An function with a variable in the exponent. Has a multiplicative rate of change
Turning point
Another name for the vertex of a parabola
Quartile
Breaks a data set into 4 equal bins each with 25%
average rate of change
Change in y over change in x; make a table using your graphing calculator to help!
slope
Constant rate of change: change in y over change in x
scatter plot
Displays the relationship between two variables. DO NOT connect the lines
Causal Relationship
Does one variable CAUSE the other variable. Remember, correlation doesn't mean causation!
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 .
Find the roots of each quadratic equation: Ex 1: y = (x - 4)(x + 3) Ex 2: y = (x + 1)(x + 2) Ex 3: y = (x - 2)(x - 3)
Ex 1: 4, -3 Ex 2: -1, -2 Ex 3: 2, 3
Determine what type of number would be an appropriate domain for each input. Ex 1: Number of Cars Ex 2: Cost in dollars Ex 3: Weight of deli meat Ex 4: Number of students
Ex 1: Positive Integers Ex 2: Positive Rational Numbers Ex 3: Positive Rational Numbers Ex 4: Positive Integers
Is Each example a function? Ex 1: {(3, 4), (2, 5), (0, 2), (-1, 4)} Ex 2: {(5, 0), (3, 2), (5, -1), (-3, 3)} Ex 3: {(-2, 1), (4, -5), (3, 4), (-6, 5)} Ex 4: {(4, 2), (3, 1), (2, 0), (2, 4)}
Ex 1: Yes Ex 2: No Ex 3: Yes Ex 4: No
Write the recursive formula Ex 1: 3, 8, 13, 18, ... Ex 2: 9, 6, 3, 0, ... Ex 3: -4, -2, 0, 2, ... Ex 4: 1, -5, -11, -17, ...
Ex 1: a₁ = 3, aₙ = aₙ-₁ + 5 Ex 2: a₁ = 9, aₙ = aₙ-₁ - 3 Ex 3: a₁ = -4, aₙ = aₙ-₁ + 2 Ex 4: a₁ = 1, aₙ = aₙ-₁ - 6
Ex 1: initial Value = 100, increase at 5% Ex 2: initial Value = 60, decrease at 5% Ex 3: initial Value = 200, increase at 12% Ex 4: initial Value = 40, decrease at 12%
Ex 1: aₙ = 100(1.05)ⁿ Ex 2: aₙ = 100(0.95)ⁿ Ex 3: aₙ = 100(1.05)ⁿ Ex 4: aₙ = 100(0.88)ⁿ
Write an explicit formula for each geometric sequence: Ex 1: 2, 6, 18, 54, ... Ex 2: 1, 4, 16, 64, ... Ex 3: 24, 12, 6, 3, ... Ex 4: 81, 27, 9, 3, ...
Ex 1: aₙ = 2(3)ⁿ⁻¹ Ex 2: aₙ = 1(4)ⁿ⁻¹ Ex 3: aₙ = 24(1/2)ⁿ⁻¹ Ex 4: aₙ = 81(1/3)ⁿ⁻¹
Write an explicit formula for each arithmetic sequence: Ex 1: 3, 9, 15, 21, ... Ex 2: 2, -4, -10, -16, ... Ex 3: 0, 3, 6, 9, 12, ... Ex 4: -3, -5, -7, -9, -11, ...
Ex 1: aₙ = 3 + 6(n - 1) Ex 2: aₙ = 2 - 6(n - 1) Ex 3: aₙ = 0 + 3(n - 1) Ex 4: aₙ = -3 - 2(n - 1)
Write the equation of a quadratic with zeros at the Given Values: Ex 1: Zeros at 4, -3 Ex 2: Zeros at 1, -2 Ex 3: Zeros at -3, -2 Ex 4: Zeros at 5, -5
Ex 1: y = (x - 4)(x + 3) Ex 2: y = (x - 1)(x + 2) Ex 3: y = (x + 3)(x + 2) Ex 4: y = (x - 5)(x + 5)
recursive function
Function that goes step by step. Start with f(1) then find f(2)...
Square root function
Function with a square root; use graphing calculator to visualize
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
What is the median in data
Is is the middle number or average of the two middle numbers AFTER THEY ARE ARRANGED IN ORDER
What is the mean in data
It is the average
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.
RANGE of a data set
Maximum # - Minimum #
elimination
Method for solving a system of equations. Add the equations together to get a variable to cancel out.
substitution
Method for solving systems of equations. Get a variable by itself and plug it into the other equation
What is the MODE in data
Most frequent number
Dot Plot
Number line with a dot for each data point above it
Irrational numbers
Numbers that can't be written as a fraction
What does a Quadratic Graph Look like
PARABOLA - The U shaped graph with a point(vertex) at the bottom or top.
Solution to a system of equations
Point(s) where two equations intersect
binomial
Polynomial with two terms Ex. (x + 4)
Where can I find cube roots on my calculator?
Press the MATH button and scroll down.
Where can I find the absolute value sign on my calculator?
Press the MATH button, scroll right to NUM and look for abs()
Arithmetic sequence
Sequence where the rate of change is additive; Look on your formula sheet for the general form aₙ = a₁ + d(n - 1) a₁ is the first term d is the common difference
Geometric sequence
Sequence where the rate of change is multiplicative; Look on your formula sheet for the general form
Solution to a system of inequalities
Shaded region where two inequalites intersect
Which ordered pair would not be a solution to y = x³ - x? 1) (-4, -60) 2) (-3, -24) 3) (-2, -6) 4) (-1, -2)
Substitute the x and y values into the equation or graph on the calculator and look at the table. Answer: 4
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
Interquartile range
The difference between Q1 and Q3
vertex
The maximum or minimum point of a parabola
coefficient
The numerical factor of a term in a polynomial. Example: 14 is the coefficient in the term 14x
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
What you do you know about the slopes of Parallel Lines
They are the same.
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
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 does the graph of an Absolute Value Function Look Like
V or upside down V
Vertical dilation (stretch) of a function
a f(x)
Horizontal Shift of a function
f(x - h) or f(x + h)
Vertical shift of a function
f(x) + k or f(x) - k
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 2 is a good model
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
sum
the result of addition
product
the result of multiplication
Axis of Symmetry
x = -b / 2a; Axis of symmetry is ALWAYS an equation x = ____
axis of symmetry
x = -b/2a ; The x value in a vertex of a parabola
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
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
standard form of a quadratic equation Ex 1: -2x² - 3x + 4 Ex 2: 5x² - 2x - 3 Ex 3: -x² + 3x + 1 Ex 4: x² - 9
y = ax² + bx + c ; a tells you whether the parabola opens up or down Ex 1: Opens Down Ex 2: Opens Up Ex 3: Opens Down Ex 4: Opens Up
slope-intercept form of a line
y = mx + b; m is the slope and b is the y-intercept.
Find the equation that models:
y intercept is 5 Slope is 2 y = 2x + 5
vertex form of a quadratic equation
y=a(x-h)² + k ; (h,k) is the vertex
Find the range y = 3x - 1 {0, 3, 7}
{-1, 8, 20}
Find the range y = 2x - 1 { 0, 4, 6}
{-1,7,11}
Identify the range {(9,-4)(2,-1)(4,7)}
{-4,-1,7}
integers
{...-4, -3, -2, -1, 0, 1, 2, 3, 4, ... }
absolute value
|n| is the distance from 0 to a number n on a number line. Ex |-3| = 3 and |5| = 5