Vocab Test Algebra II Flashcards
Arithmetic Sequence
A sequence in which the difference of consecutive terms is constant
Asymptote
A line that a graph approaches more and more closely
Change of Base Formula
Log a B=Log B/Log A
Combined Variation
a combination of direct and inverse variation: y=kx/z.
Common Difference
The constant difference d between consecutive terms of an arithmetic sequence
Common Logarithm
Logarithm with base 10
Common Ratio
The constant ratio t between consecutive terms of a geometric sequence
Completing the Square
To add a term c to an expression of the form x^2 + bx such that x^2 +bx + c is a perfect square trinomial
Complex Conjugates
Pairs fo complex numbers of the forms a + bi and a - bi, where b does not = 0
Complex Fraction
A fraction that contains a fraction in its numerator or denominator
Complex Number
a number that can be expressed in the form a + bi, where a and b are real numbers
Composition of Functions
an operation that takes two functions f and g and produces a function h
Compound Inequality
the overlap or intersection of the solution sets for the individual statements.
Conic Section
a curve obtained as the intersection of the surface of a cone with a plane
Consistent
a linear or nonlinear system of equations
Constant of Variation
the constant (unchanged) ratio of two variable quantities. where k is the constant of variation
Continuous Relation
A set of data is said to be discrete if the values belonging to the set are distinct and separate
Correlation Coefficient
A number that is a measure of the strength and direction of the correlation between two variables
Dependent
depends on the value of some other number
Dimensions of a Matrix
the number of rows by the number of columns
Direct Variation
simple relationship between two variables
Discriminant
the part of the quadratic formula underneath the square root symbol
Ellipse
regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points is constant
End Behavior
The end behavior of a function f describes the behavior of the graph of the function at the “ends” of the x-axis
Exponential Equation
a function of the form {\displaystyle f(x)=ab^{x}, } where b is a positive real number, and the argument x occurs as an exponent
Extraneous Solution
a solution that emerges from the process of solving the problem but is not a valid
Extrema
the maximum or minimum value of a function.
Factor Theorem
a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f(k)=0
Finite Sequence
a list of terms in a specific order
Function
a function that can be defined as the root of a polynomial equation
Geometric Sequence
a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Greatest Integer Function
a function that returns a constant value for each specific interval
Inverse Variation
y varies inversely as x if there is some nonzero constant k such that
Joint Variation
a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant.
Latus Rectum
the chord through a focus parallel to the conic section directrix
Linear Programming
a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
Logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Logistic Growth Model
The logistic growth model is approximately exponential at first, but it has a reduced rate of growth as the output approaches the model’s upper bound, called the carrying capacity.
Matrix
a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns
nth root
it is the general way of talking about roots
Natural Logarithms
Logarithm with base 10
Negative Exponent
just means that the base is on the wrong side of the fraction line
Parabola
a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape
Parent Function
the simplest function of a family of functions that preserves the definition of the entire family
Piece Wise Defined Function
a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain
Point Slope Form
y − y1 = m(x − x1)
Quadratic Function
a function of degree two
Radicand
he value inside the radical symbol
Rate of Change
the speed at which a variable changes over a specific period of time.
Rational Exponent
an exponent that is a fraction
Rational Function
any function which can be written as the ratio of two polynomial functions
Rationalizing the Denominator
means to eliminate any radical expressions in the denominator such as square roots and cube roots
Recursive Formula
a formula that defines each term of a sequence using preceding term(s)
Regression Line
a straight line that de- scribes how a response variable y changes as an explanatory variable x changes.
Relative Maximum
a point where the function changes direction from increasing to decreasing
Relative Minimum
is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood
Root
The root of a number x is another number, which when multiplied by itself a given number of times, equals x
Scatter Plot
a two-dimensional graphical representation of a set of data.
Sequence
an enumerated collection of objects in which repetitions are allowed and order matters
Set-Builder Notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements
Step Function
a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals.
Synthetic division
synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division
Vertex Form
The vertex form of a quadratic is given by y = a(x – h)2 + k, where (h, k) is the vertex
Vertical Line Test
a method that is used to determine whether a given relation is a function or not
Zeros
no quantity or number; naught; the figure 0.
