Precal 3.1, 3.3, 4.1, 4.3, 4.4

Front 1

quadratic function

Back 1

function of the form f(x)=ax^2+bx+c

Front 2

formula for 1st coordinate of vertex of parabola

Back 2

-b
-------
2a

Front 3

quadratic formula

Back 3

-b+- sq.rt.(b^-2ac)
------------------------
2a

Front 4

discriminant

Back 4

b^2-2ac

Front 5

projectile motion formula

Back 5

y=16t^2+v0t+h

v0=initial velocity
h=initial height

Front 6

power function

Back 6

function of the form f(x)=ax^n where a,n are constants

Front 7

polynomial function

Back 7

function of the form f(x)=a sub(n)x^n+a sub(n=1)x^(n-1)+...+a sub(1)x+a sub(0)

Front 8

continuous on an interval (informal)

Back 8

?????MAGIC?????

Front 9

zero of a function

Back 9

any number z such that f(z)=0

Front 10

multiplicity of a zero z

Back 10

largest exponent k such that (x-z)^k is a factor of he polynomial

Front 11

division algorithm

Back 11

If f(x) and g(x) denote polynomial functions and if g(x) is no the zero polynomial, then ether are unique polynomial functions q(x) and r(x) such that f(x)= q(x)g(x) + r(x)

Front 12

remainder theorem

Back 12

If polynomial f(x) is divided by x-c, then the remainder is f(c)

Front 13

factor theorem

Back 13

x-c is a factor of polymial f(x) iff f(c)=0

Front 14

decartes' rule of signs

Back 14

Let f be a polynomail fnction.
1) the # of positive real zeros of f equals the # of sign variations of the coefficionts of f(x), or less than this by an even #
2)the number of negative real zeros of f equals the # of sign variations of the coefficients of f(-x), or less than this by an even number.

Front 15

rational zeros theorem

Back 15

theoremlet f by a polynomial function with integral coefficients. If p/q (in lowest terms) is a rational zero of f, then p must be a factor of the costant term, and q must be a factor of the leading coefficient.

Front 16

Upper Bound Test

Back 16

Let f be a polynomial function with positive (negative) leading coefficient, and c be a positive number. If the resulst of substituting c snthetically into f yields non-negative (non-positive) numbers, then c is an upper bound for the zeros of f.

Front 17

Lower Bound Test

Back 17

Let f be a polynomial function, and c be a negative number. If the result of substituting c synthetically into f yields numbers alternating in sign (0 may be considered eithrer + or -), then c is a lower bound for the zeros of f.

Front 18

leading term

Back 18

...................

Front 19

leading coefficient

Back 19

.........................

Front 20

complex number

Back 20

# of the form a+bi where a,b E R and i=sq.rt. (-1)

Front 21

Imaginary number

Back 21

..........................

Front 22

complex polynomial function

Back 22

(same as polynomial function) except the coefficients are complex #'s)

Front 23

Linear Factorization Theorem

Back 23

Every complex polynomial function f(x) of degree n>=1 can be factored into n liner factors (not necessarily distinct) of the form f(x) = a sub.n(x-r1)(x-r2)...(x-rn) where a sub.n, r1, r2.....,rn are complex numbers

Front 24

Conjugate Pairs Theorem

Back 24

If f is a polynomial function and a+bi where b does not =0 is a zero of f, then a-bi is also a zero

Front 25

Odd Degree Corollary

Back 25

If f is a polynomial function w/ odd degree, then f must have at least 1 real zero

Front 26

Locater Theorem

Back 26

If f is a polynomial function, and a,b E R such that f(a) and f(b) have opposite signs, then there is at least 1 zero of f between a and b.

Front 27

Intermediate Value Theorem

Back 27

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