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