Math Chapter 2 Vocab

The theorem that can be used to determine the possible numbers of positive and negative real zeros of a function is called ___ ___ ___ ___.

Descartes' Rule of Signs

The graph of a quadratic function is symmetric about its ___.

axis

The numbers a+bi and a-bi are called ___ ___ and their product is a real number a^2+b^2.

complex conjugates

If a+bi is a complex zero of a polynomial with real coefficients, then so is its ___, a-bi.

conjugate

Graphs of all polynomials are ___, which means they have no breaks or gaps.

continuous

To solve a polynomial inequality, find the ___ numbers of the polynomial, and use these numbers to create ___ ___ for the inequality.

critical, test intervals

The ___ theorem states that polynomial f(x) has the factor (x-k) if and only if f(k)=0.

factor

The ___ ___ ___ ___ states that if f(x) is a polynomial, then f has at least 1 zero in the complex number system.

fundamental theory of algebra

If f(x)->b as x->+-infinity, then y=b is a ___ ___ of graph f.

horizontal asymptote

a+bi, a/=0, b/=0 is an ___ ___.

imaginary number

The rational expression p(x)/q(x) is called ___ if the numerator is greater than or equal to that of the denominater, and is called ___ if the degree of the numerator is less than that of the denominator.

improper, proper

The ___ ___ ___ states that if f is a polynomial such that f(a)=/ f(b), then the interval (a, b), f takes on every value between f(a) and f(b).

intermediate value theorem

A quadratic factor that cannot be factored further as a product of linear factors containing real numbers is said to be ___ over the ___.

irreducible, reals

The ___ ___ ___ is used to determine the left and right hand behavior of the graph of a polynomial.

leading coefficient test

The ___ ___ ___ states that if f(x) is a polynomial, then n has exactly n linear factors.

linear factorization theorem

A real number b is ___ bound for the real zeros of f if no real zeros are less than b, and is an ___ bound if no real zeros are greater than b.

lower, upper

A polynomial of degree n has at most ___ real zeros and ___ turning points.

n, n-1

If the graph of a quadratic function opens downward, then the leading coefficient is ___ and the vertex is a ___.

negative, maximum

A polynomial function of degree n and leading coefficient an is a function of the form f(x)=anx^n+... a1x+a0 where n is a ___ ___ and a1 is a ___ number.

nonnegative integer, real

If the graph of a quadratic function opens upward, then the leading coefficient is ___ and the vertex is a ___.

positive, minimum

a+bi, a=0, b/=0 is a ___ ___ ___.

pure imaginary number

A ___ function is a second degree polynomial, and its graph is called a ___.

quadratic, parabola

Functions of the form n(x)/d(x), where n(x) and d(x) are polynomials and d(x) is not 0 are called ___ ___.

rational functions

The test that gives a list of the possible rational zeros of a polynomial function is called the ___ ___ test.

rational zero

a+bi, b=0 is a ___ ___.

real number

The ___ theorem states that if a polynomial f(x) is divided by x-k, the remainder is r=f(k).

remainder

For the rational function n(x)/d(x), if the degree of n(x) is exactly one more than the degree of d(x), then the graph of f has a ___ ___.

slant asymptote

If x=a is a zero, then the following is true: x=a is a ___ of the equation. (x-a) is a ___ of the equation. (a, 0) is an ___-___ of the graph.

solution, factor, x-intercept

i is defined as the ___ ___ of -1, where i^2 equals ___.

square root, -1

A polynomial is written in ___ form if terms are in descending order of exponents.

standard

An alternative method to long division of polynomials is called ___ ___, in which the divisor must be of the form (x-k).

synthetic division

If a real zero of a polynomial is of even multiplicity, then the graph of f ___ the x axis of x=a, and if it is of an odd multiplicity then it ___ the axis at x=a.

touches, crosses

If f(x)->+-infinity as x->a from the left or right, then x=a is a ___ ___ of graph f.

vertical asymptote

The critical numbers of a rational expression are its ___ and its ___ ___.

zeros, undefined values

The formula that relates cost, revenue and profit is ___.

P=R-C