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Algebra 1 Regents Vocabulary
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Gravity
Key Concepts:
Terms in this set (140)
"a" in y = a•b^x
the variable used to represent the initial amount in an exponential function
"b" in y = a•b^x
the variable used to represent the growth rate in an exponential function
"b" in y = mx + b
the variable used to represent the y-intercept in a linear function
"m" in y = mx + b
the variable used to represent the slope of a line
Absolute value
the distance a number is from zero (y=|x|)
Algebraic expression
contains numbers, variables, and operations (no equal sign)
Area
the amount of space within a 2-dimensional figure
Associative property
(a+b)+c=a+(b+c)
Axis of symmetry
a line that divides a parabola in two equal halves and goes through the vertex
Binomial
an expression that contains two terms
Coefficient
the "big" number in front of the variable
Common difference
the constant difference between consecutive terms in a sequence
Common ratio
the ratio of a term in a geometric sequence with the previous term (1:2 = 1/2)
Commutative property
a+b=b+a
Constant of variation
the "k" value that remains the same in direct (y = kx) or inverse variation (xy = k)
Constant term
a term with no variable part; a value that stays the same (2x + 3 where 3 is the constant term)
Coordinates
the ordered pair that represents a point (x, y)
Correlation
the relationship between a set of data; it can be positive, negative, constant, or no correlation
Decay rate
the rate at which an exponential function is reduced
Denominator
the bottom part of a fraction
Dependent variable
the variable (output) that depends on the value of the independent variable (input) - "Cost" is the dependent variable in this situation.
Difference
the answer to subtraction
Distributive property
a(b + c) = ab + ac
Domain of a function
all the possible x-values of a function (The domain of this situation is {1, 2, 3, ...}
Elimination
used to solve a system of equations by adding the two equations in order to cancel out one of the variables
Equation
has an equal sign
Equivalent expressions
two expressions that are equal (3x + 5 = 2x - 6)
Evaluate
to find the value of an expression by substituting a numbers in for the variables
Exponential decay
a situation that decreases by the same factor each time; the growth rate is 0 < b < 1
Exponential function
Exponential growth
a situation that increases by the same factor each time; the growth rate is b > 1
Factor
an expression that is part of a product; (2x - 1) and (x - 1) are factors
Factor completely
to factor a polynomial until all factors are prime
Factoring
to find the factors of a polynomial; (2x-1)(x-1) is the factored form
Formula
an equation that can be used to find a specified value
Function
for every input (x) there is only one output (y); All the x-values have to be different The y-values don't matter.
Function notation
uses f(x) instead of y; f(x) = 3x + 5
Function rule
an expression that can be used to represent a functional set of data
Graph of a system of linear inequalities
the intersection area of two or more linear inequalities
Graph of an equation in two variables
forms a line on a coordinate plane
Graph of an inequality in one variable
the solution to an inequality that can be represented on a number line
Graph of an inequality in two variables
forms a shaded area on a coordinate plane with a boundary line
Greatest Common Factor
the biggest term that can be divided into all terms
Growth rate
the rate at which an exponential function is increased
Horizontal
a line that goes left-right parallel to the x-axis
Independent variable
the variable (input) that determines the dependent variable (output); "Toppings" is the independent variable.
Inequality
contains an inequality symbol
Infinite solutions
a system of equations in which all values are true (the equations are the same line)
Initial value
the beginning amount in an exponential function represented by the letter "a"
Input
the x-values (domain) of a relationship; (0 and 1 are the input values)
Integers
numbers that belong to the set ... -3, -2, -1, 0, 1, 2, 3 ...
Intersection
the point where two equations "cross" each other
Inverse operations
opposite operations (+ and - or * and / )
Irrational numbers
numbers than cannot be written as a fraction
Leading coefficient
the coefficient of the first term when a polynomial is written so that the exponents decrease from left to right; 2 is the leading coefficient
Like terms
terms that have the same variable parts
Line of best fit
a line used to model a trend in a set of data
Linear equation
an equation whose graph is a straight line
Linear function
a function that can be represented by a line that is not vertical
Linear inequality in two variables
a line in which the equal sign is replaced with an inequality symbol
Linear regression
the process that finds the best-fitting line to model a set of data (can be done on the calculator)
Linear system
two or more linear equations that have the same variables
Literal equation
an equation where letters are used to represent numbers (A=lw)
Mapping
a diagram that uses arrows to connect the input with the corresponding output values
Maximum value
the y-value of the vertex of a parabola
Mean
the average of a set of data
Median
the middle number of a set of data that has been ordered from least to greatest
Midpoint
the point on a line that is equidistant from the endpoints (the exact middle)
Minimum value
the y-value of the vertex of a parabola
Mode
the number(s) that occur the most in a set of data
Monomial
a polynomial with only one term
Negative exponent
No solution
a system of equations in which there are no solutions (the lines are parallel)
Numerator
the top part of a fraction
Opposites
positive/negative; multiplication/division; addition/subtraction
Order of operations
rules for evaluating an expression (PEMDAS)
Ordered Pair
the coordinates of a point (x, y)
Origin
(0, 0)
Output
the y-values (range) of a situation (6 and 6.50 are the output values)
Parabola
the "U" shaped graph of a quadratic equation
Linear parent function
y=x
Quadratic parent function
y=x^2
Percent of change
the percent a quantity increases/decreases;
Percent of decrease
the percent of change when the new amount is less than the original amount
Percent of increase
the percent of change when the new amount is more than the original amount
Perfect square
a number that has a whole number square root; 1=1(1); 4=2(2); 9=3(3); 16=4(4) so, 1, 4, 9, 16,... are perfect squares
Perimeter
the distance around a figure
Polynomial
a monomial or sum of monomials
Product
the answer of multiplication
Proportion
an equation that states to ratios are equal; x/60 = 5/4
Quadratic formula
the formula used to find the solutions of a quadratic equation
Quadratic function
an equation that can be written in the form above
Quotient
the answer to division
Range of a data set
the difference between the biggest and smallest values in a set of data; Range = {6, 6.50, 7, 7.50,...}
Range of a function
all the possible y-values of a function; Range = {6, 6.50}
Rate
a fraction that compares two quantities measured in different units (miles per hour)
Rate of change
the slope of a line
Ratio
the comparison of two numbers using division (6:4 or 6/4)
Rational numbers
numbers that can be expressed as a fraction (i.e: 1/3)
Real numbers
the set of all rational and irrational numbers
Reasonable Range
the range that takes into account the restrictions of a situation
Relation
the pairing of inputs with outputs
Roots
the solution to an equation; where the graph crosses the x-axis
Scatter plot
a graphing of points to determine if data has a relationship
Scientific notation
a number written in the form c x 10^n where 1 <= c < 10 and n is an integer
Simplify
to perform all indicated operations
Slope
rate of change which is the vertical change (rise) over the horizontal change (run) in a line
Slope-intercept form
an equation in the form y = mx + b
Solution of a system of linear equations
an ordered pair that is a solution to all of the equations in the system;The solution is (-4,2)
Solution of a system of linear inequalities
an ordered pair that is a solution to all of the inequalities in the system (in the shaded region)
Solution of an equation in one variable
a number that makes a true statement when substituted into an equation
Solution of an equation in two variables
an ordered pair that makes a true statement when substituted into an equation
Solution of an inequality in one variable
a number that makes a true statement when substituted into an inequality
Solution of an inequality in two variables
an ordered pair that makes a true statement when substituted into an inequality (any coordinate in the shaded region)
Square root
b is the square root of b(b)
Standard form of a quadratic equation
Substitution
used to solve a system of equations by substituting the expression for one variable in for that variable for the other equation
Sum
the answer to addition
System of linear equations
two or more equations using the same variables
System of linear inequalities in two variables
two or more linear inequalities using the same variables
Terms of an expression
parts of an expression separated by a + or - sign
Trinomial
a polynomial with three terms
Undefined slope
the slope of a vertical line
Unit rate
a rate in which the denominator is 1
Variable
a letter used to represent a number
Vertex of a parabola
the minimum or maximum point of a parabola
Vertical line
a line that goes up and down perpendicular to the x-axis
Vertical line test
a test in order to determine if graph is a function by seeing if a vertical line can be placed anywhere on the graph and it will only pass through one point
Whole numbers
the numbers 0, 1, 2, ...
x-axis
the horizontal axis on a coordinate plane
x-intercept
the point where the graph crosses the x-axis; the y-value will always be zero
y-axis
the vertical axis on a coordinate plane
y-intercept
the point where the graph crosses the y-axis; the x-value will always be zero
Zero exponent
Zero of a function
where the graph crosses the x-axis; the x-value for which f(x) = 0 (or y = 0)
Less than
<
Greater than
>
Less than or equal to
Greater than or equal to
Prime
is only divisible by 1 and itself
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