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NYS Algebra Regents Vocabulary Review
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Gravity
Key Concepts:
Terms in this set (97)
rational
number that can be expressed as an integer or fraction; a number with a terminating decimal
Ex: 6.2
continuous graph
allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values.
Ex: When x = 1.2, y = 3, when input = 1.2, output = 3, or (1.2 , 3) as an ordered pair
maximum turning point
a relative maximum value in a polynomial function; the y value or output where the graph starts to decrease
absolute value
value or distance away from zero
discrete graph
allows the x-values to be only certain points in the interval, usually only integers or whole numbers
Ex: When x = 1, y = 3, when input = 1, output = 3, or (1, 3) as an ordered pair
sum
to add
Ex: the sum of 2 and 2 = 4
monomial
one term
Ex: 12, 12xy, or x
function
a relation where for every input, there is exactly one output; can be tested with the vertical line test
Ex: x=3 y=2
x=2 y=1
x=1 y=0
x=0 y=1
causation
the ability of one variable to influence another
Ex: the input or x value determines the output or y value
bivariate data
data on each of two variables, where each value of one of the variables is paired with a value of the other variable
conjugate pair
two binomials that are the same except for different signs
Ex: (2x+4)(2x-4)
quartiles
four equal groups in a data set; the median separates the upper and lower quartiles; the median of the lower quartiles separates quartile 1 and quartile 2; the median of the upper quartile separates quartiles 3 + 4
zero property factor
When the product of two real numbers is 0, at least one of them is 0; used to justify the process of factoring
irrational
number that cannot be expressed as an integer or fraction; a number with a terminating decimal
Ex: π or the number pi
linear
having a graph with a straight line; a function where all variables are raised to the power of 1; functions with a constant rate of change
Ex: y=x, y=mx+b, y=3x+7, or 2x-3y=16
minimum turning point
a relative minimum value in a polynomial function; the y value or output where the graph starts to increase
substitution method
used to solve a linear system for one or more variables; where one variable is solved for and then plugged in to find the value of the second
Ex: 3x+y = 10 and 2x+ 2y = 8
1) Solve for y
2) Plug in y value in second equation
3) Solve for x
4) Plug in x value in first equation for y
constraints
limitations or restrictions placed on variables
Ex: inequality signs (cannot be more than or less than)
turning point
value(s) in a polynomial function that show a change in direction; the y value or output in the graph, where the graph starts to increase or decrease
interval notation
representing an interval as a pair of numbers; x values or inputs with corresponding outputs that make an inequality true
linear regression
linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables) with a line of best fit
multiplicative property of equality
property of equality that allows one to multiply the same quantity by both sides of an equation and for both sides to still be equal
Ex: x= 4 multiplied by 2 on each side is 2(x)= 2(4)
symmetry
when two or more parts are identical after a flip, slide or turn; when two sides are identical, mirror images
recursive definition
a formula that uses the preceding term to define the next term of a sequence; sequences can have the same formula but because they start with a different number, they result in different patterns
rate of growth
the value that the function increases by over a course of time
Ex: a positive slope of a line
elimination method
used to solve a linear system for one or more variables; where one variable is "cancelled" when the functions are added and then the second variable is solved for
Ex: 3x+y = 10 and 2x+ 2y = 8
1) Multiple the 2st equation by -2
2) Add the equations together to cancel the y variable
3) Solve for x
4) Plug in x value in first equation for y value
parameter
a quantity that influences the output or behavior of a mathematical term but is viewed as being held constant
Ex: in y=mx+b, m and b are parameters
quoitent
the answer after you divide one number by another
trinomial
a mathematical expression with 3 terms or 3 monomials
Ex: ax^2 + bx + c
range
all possible y values or outputs in a function
residual
difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line)
square root
a number that produces a specified quantity when multiplied by itself
Ex: the square root of 49 is 7
axis of symmetry
the x value or input that creates a line through a shape so that each side is a mirror image
common ratio
the ratio between two numbers in a geometric sequence; ratio is usually indicated by the variable r.
Ex: The geometric series 3, 6, 12, 24, 48, ... has common ratio r = 2
additive property of equality
the property that states that if the same amount is added to both sides of an equation, then both sides are still equal
Ex: if x= 4, then both sides + 2, is x+2 = 4+2
explicit graph
created from a sequence using n, or where n is the number location of each term in a sequence
Ex: f (n) = 5n + 5
factor
one of two or more numbers, algebraic expressions, etc., that when multiplied together result in a product
Ex: factors of 18 are (1)(18), (2)(9), and (3)(6)
rate of decay
the value that the function decreases by over a course of time
Ex: a negative slope of a line
quadratic
having a graph with one or more "U" shapes; a function where all variables are raised to the power of 2; functions with a exponential rate of change
Ex: y=x^2 or y=a(b)^x
exponential
functions containing one or more numbers or quantities raised to an exponent
Ex: 3x^5= 9
difference
to subtract
Ex: the difference of 7 and 2 is 5
associative property
to change the grouping or (_) of the terms in an equation
Ex: from 2x+3x+4 = 18 to (2x+3x)+4=18
standard deviation
a measure of how spread out numbers are in a data set from the median
commutative property
to change the order of the terms in an equation
Ex: from 2x+3x+4 = 18 to 2x+4+3x = 18
average rate of change
the constant value of increase or decrease between two points in a function; the change in y divided by the change in x; the slope
distributive property
when multiplication is applied to the addition of two or more numbers in a parentheses by a factor outside the parentheses
Ex: a(b + c) = ab + ac
common difference
the difference between two numbers in an arithmetic sequence
Algebraic Expression
A mathematical phrase that can include numbers, variables, and operation symbols
Constant
A term that has no variable factor
Correlation coefficient
r, which tells you how closely the equation models the data
Dependent variable
depends on the value of the independent variable
Domain
the possible values for the input, or the independent variable, of a function
Element
each item in a matrix
Equation
A mathematical sentence that uses an equal sign
Function
a relationship that assigns exactly one output value for each input value
Function Notation
when you use f(x) to indicate the outputs
Function rule
an equation that describes a functional relationsip
Hypotenuse
The side opposite the right angle in a right triangle
Identity
An equation that is true for every value
Independent Variable
a variable that provides the input values of a function
Inequality
A mathematical sentence that compares the values of 2 expressions using an inequality symbol
Integers
whole numbers and their opposites
Inverse Operations
operations that undo one another
Irrational Number
A number that cannot be written as a ratio of 2 integers. They are nonterminating and nonrepeating in decimal form
Matrix
a rectangular arrangement of numbers in rows and columns
Leg
Each of the sides that form the right angle of a right triangle
Like terms
Terms with exactly the same variable factors in a variable expression
Line of Best Fit
The trend line that shows the relationship between 2 sets of data most accurately
Linear Equation
an equation whose graph is a line
Perfect Square
Numbers whose square roots are integers
Range
The difference between the greatest and the least data values for a set of data
Rate of Change
allows you to see the relationship between two quantities that are changing
Ratio
a comparison of two numbers by divison
Rational Number
A real number that can be written as a ratio of 2 integers. They are terminating or repeating in decimal form.
Relation
a set of ordered pairs
Simplify
Replace an expression with its simplest name or form
Slope
the ratio of the vertical change to the horizontal change
Vertical-Line-Test
Used to tell whether a relation is a function from a graph
x-intercept
the x-coordinate of the point where a line crossed the x-axis
y-intercept
the y-coordinate of the point where a line crossed the y-axis
Axis of Symmetry
The line that divides a parabola into 2 matching halves
Binomial
A polynomila of 2 terms
Discriminant
The quantity b^2-4ac is the discriminant of ax^2+bx+c=0
Infinitely Many Solutions
The number of solutions of a system of equations in which the graphs of the equations are the same line
Monomial
an expression that is a number, a variable, or a product of a number and one or more variables
Parabola
The graph of a quadratic function
No solution
when the graphs of the equations in a system are parallet with no point of intersection
Proportion
an equation that states that two ratios are equal. a/b=c/d where b is not eqaul to 0 and d is not eqaul to 0
Quadratic Function
A function of the form y-ax^3+bx+c, where a is not equal to 0. The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down
Quadratic Equation
An equation you can write in the standard form ax^3+bx+c=o, where a is not equal to 0
Roots (of the equation)
The solutions of an equation
Term
A number, variable, or the product of quotient of a number and one or more variables
Trinomial
A polynomial of 3 terms
Unit Analysis
The process of selecting conversion factors to produce the appropriate units
Vertexs
The highest or lowest point on a parabola. the axis of symmetry intersects the parabola at the vertex
Zero (of the function)
The x-intercept of the graph of a function
Evaluate
substitute a given number for each variable, and then simply
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