Chapter 2 math vocab

principal square

if a is a positive number, the ... root of the negative number -a is defined as √-a= i√a

touches

if a real zero of a polynomial func of even multiplicity, then the graph of f ... the x-axis at x=a

crosses

If a real zero of a polynomial func of odd multiplicity, then the graph of f ... the x-axis at x=a

nonnegative integer; real number

a polynomial function of degree n and leading coefficient an, is a function of the form f(x)=anxn...an-1+...+a1x+a0 when n is a ... and a1 are ...

n;n-1

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

irreducible over the reals

a quadratic factor that cant be factored further as a product of linear factors containing real numbers is said to be... over the...

lower; upper

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

imaginary number

a+bi, a and b not equal to 0

pure imaginary number

a+bi, a=0, b not equal to 0

real number

a+bi, b=0

synthetic division

an alternative method to long division of polynomials is ...., in which the divisor must be of the form x-k

Descartes' Rule of Signs

can be used to determine the possible numbers of positive numbers of positive real zeros and negative real zeros of a func

Division Alorithm dividend, divisor, quotient, remainder

f(x)=d(x)q(x)+r(x) what is this called name terms

slanted asymtote

for the rational func if the degree of N(x) is exactly one more than the degree of D(x) then the graph has a ...(or oblique)

standard form

form of a polynomial func when its terms are written in descending order of exponents form left to right

rational functions

func 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

axis

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

continuous

graphs of all polynomials are ..., which means they have no breaks, holes, or gaps

-1

i^2=

conjugate

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

vertical asymtote

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

horizontal asymtote

if f(x) arrow b as x arrow +- infinity, then y=b is a ... of the graph

negative; maximum

if the graph of a quadratic function opens down, then its leading coefficient is... and the vertex of the graph is a ...

positive; minimum

if the graph of a quadratic function opens up, then its leading coefficient is .. and the vertex of the graph is a ...

solution; (x-a); x-intercept

if x=a is a zero: x=a is a ... of of polynomial equation f(x)=0 ... is a factor of the polynomial f(x) (a,0) is an ... of graph f

the factor theorem

sates that a polynomial f(x) has a factor (x-k) if and only if f(k)=0

quadratic function; parabola

second-degree polynomial function with a graph called a ...

the remainder theorem

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

Intermediate Value Theorem

states that if f is a polynomial func such that f(a) is not equal to f(b), then in the interval [a,b), f takes on every value between f(a) and f (b)

Fundamental Theorem of Algebra

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

Linear Factorization Theorem

states that if f(x) is a polynomial of degree n, then f has precisely n linear factors f(x)=an(x-c1)(x-c2)...(X-cn where c1,c2,...cn are complex numbers

zeros and undefined values

the critical numbers of a rational expression are its.. and ...

P=R-C

the formula that relates cost, revenue and profit

√-1

the imaginary unit i is defined a i=

complex conjugates

the numbers a+bi and a-bi; their product is a^2+b^2

improper; proper

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 that of the denom

Rational Zero Test

the test that gives a a list of possible rational zeros of a polynomial func

critical; test intervals

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

leading coefficient test

used to determine the left and right-hand behavior of the graph of a polynomial function