Math Vocab Ch. 2

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 positive number, the ___ root of the negative number -a is defined as square root of -a = square root of a then i.

Complex numbers, a+bi

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

Conjugate

The graphs of all polynomial functions are ____, which means that the graphs have no breaks, holes, 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 that can be used to determine the possible numbers of positive real zeros and negative real zeros of a function is called ___ of ___.

Descartes' Rule of Signs

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

Factor

The ___ of ___ states that if f(x) is a polynomial of degree n (n is greater than 0), then f has at least one zero in the complex number system.

Fundamental Theorem of Algebra

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

Horizontal Asymptote

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

Improper, Proper

The ___ Theorem states that is f is a polynomial function such that f(a) cannot =f(b), then in the interval [a,b], f takes on every value between f(a) and f(b).

Intermediate Value

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

Irreducible over the reals

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

Leading Coefficient Test

A real number b is an ___ 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

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

Negative, Maximum

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

P=R-C

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

Positive, Minimum

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

Quadratic, Parabola

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

Rational Zero

Functions of the form f(x)=N(x)/D(x), where N(x) and D(x) are polynomials and D(x) is not the zero polynomial, are called ___.

Rational functions

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 given by f(x)=N(x)/D(x), if the degree of N(x) is exactly one more than the degree of D(x), the the graph of f has a ___ (or oblique) ___.

Slant Asymptote

If x=a is a zero of a polynomial function f, then the following three statements are true. a) x=a is a ___ of the polynomial equation f(x)=0 b) ___ is a factor of the polynomial f(x) c) (a,0) is an ___ of the graph f

Solution, x-a, x-intercept

The imaginary unit i is defined as i=___, where i^2=___.

Square root of -1, -1

A polynomial function is written in ___ form if its terms are written in descending order of exponents from left to right.

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 function is of even multiplicity, then the graph of f ___ the x-axis at x=a, and if it is of odd multiplicity then the graph of f ___ the x-axis at x=a.

Touches, Crosses

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

Vertical asymptote

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

Zeros, undefined values

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

n, n-1