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
