Programs for Algebra II courses, esp. those using the big green book.
Michael Castleman, mlc@sri.kbt.com

What are these programs?
------------------------
        These programs are designed to make the lives of Algebra II students
just a bit easier. Although they are especially designed for use with the
book by Paul A. Foerster called _Algebra_and_Trigonometry:_Functions_and_
_Applications_, (it's big and green) they will probably be of use to all
Algebra II students.

Why three programs?
-------------------
        Each program corresponds to one chapter of the math book. For those
of you with different books, we have:
                CHAP5   Quadratic Functions and Complex Functions
                CHAP6   Exponential and Logarithmic Functions
                CHAP7   Rational Algebraic Functions
                CHAP8   Irrational Algebraic Functions (not really; see below)
        As I get through the year, you can probably expect me to write more
programs :)

Any general instructions?
-------------------------
        Upon starting each program, you will be presented with a menu of
all modules within each program. Select a module and follow the directions.
I tried to be reasonably clear, but if you have any trouble, refer to this
document.

CHAP5 - PARABOLA
----------------
        When you run this module, you are prompted for A, B, and C in the
function F(X)=AX\^2\+BX+C. Enter them in, and you will be presented with the
coordinates of the vertex (H, K), the coordinates of a symetric point (SX, SY)
(useful for graphing), the Y intercept (YI), and any real X intercepts that
may exist (XI). Then, press [ENTER], and the parabola will be graphed.

CHAP5 - IQUAD
-------------
        This really stands for Improved QUADformula, but you can pretend it
stands for Imaginary QUADformula if you wish. Give it A, B, and C in the
equation AX\^2\+BX+C = 0, and it will give you a display of the form
                        +----------------+
                        | X    +-|Z      |
                        |----------------|
                        |   Y            |
                        |                |
                        |               N|
                        |+-             O|
                        +----------------+
Where X, Y, and Z are the parts of the Quadratic Formula (Z is the discrimant
if you have to know), and the answers are N+O and N-O. If you see an I in the
third column of the last line, the answers are N+Oi and N-Oi, where i=\sqrt\-1

CHAP5 - QUADPNTS
----------------
        This finds the particular equation of the parabola passing through
(x1,y1), (x2,y2), and (x3,y3). Enter the x's and y's when prompted, and,
unless there is no parabola passing through those three points, you will be
given A, B, and C.

CHAP5 - SPLINE
--------------
        This is just like QUADPNTS, but works for any number of points. If
you enter N points, the numbers given back to you will be the coefficiants
of X^(N-1), X^(N-2), X^(N-3), and so on, down to X and 1. This is actually
sounds a lot more complicated than it is.

CHAP6 - EXSOLVEI
----------------
        This solves the equation A^X=B for X with a known A and B using an
iterative method. This is a complete waste of time, but my math teacher made
me write it. Provide A and B, and then give it a guess and the number of
decimal places you wish. Note that your guess must be an integer *less* than 
the correct answer. Use zero if you're not sure. If this is too confusing
for you, or even if it's not, use EXSOLVEL; it's better.

CHAP6 - EXSOLVEL
----------------
        This solves the equation A^X=B for X with a known A and B using a
logarithmic method. This is much better than the method used in EXSOLVEI.
Give it A and B, and it gives you the answer. Viola.

CHAP6 - LOGFUNCS
----------------
        This can solve the equation
                Y = log  X
                       b
for either b, X, or Y, assuming you know the other two. Use the menu to tell
it which two variables you know, enter them in, and it will pop out the
value of the third variable.

CHAP6 - AMPROP
--------------
        This deals with the Add-Multiply Property of Exponential Functions.
If you have an exponential equation of the form f(x)=ab^x, and you know two
points on the function, this program uses the Add-Multiply property to find
four more points. They are displayed in a table, with the X values in the
left-hand column, and the values for f(x) displayed on the right.

CHAP6 - EXPREG
--------------
        Given two points on an exponential equation's graph, this program
will find the particular equation of the curve. Give it (X1,Y1) and (X2,Y2),
and it spouts back a and b from the equation Y=ab^x.


CHAP7 - FACTORG
---------------
        This is the text to 'Mr. Cronin's Guide to Factoring', a guide my
math teacher (Mr. Cronin) put on the board one day and I typed into the
calculator. While it can't actually do anything _for_ you, it contains some
examples and tells you how to factor all kinds of things. Oh, and if you read
_The_Hitchhiker's_Guide_to_the_Galaxy_, then you get the joke.

CHAP7 - POLYMULT
----------------
        This multiplies polynomials. It can do (ax+b)(cx+d),(ax^2+bx+c)(ex+f),
(ax+b)(cx+d)(ex+f), and (ax^2+bx+c)(dx^2+ex+f). Tell it the number of terms
and the factors, and it multiplys them. The coefficiants are on the right and
the x^n's are on the left, but you'll be able to figure it out.

CHAP7 - RABBIT
--------------
        This tries pull a rabbit out of a hat. I included this because of
a problem which wanted you to factor a rabbit out of (x+y). The joke's from
the TV show "Rocky & Bullwinkle. If you don't get it, tough. OK, I admit it,
it has nothing to do with math. Sorry.

CHAP7 - FACTTHER
----------------
        This attempts to find all factors of the form (AX+B) from any
polynomial of up to 5 terms. Tell it how many terms, enter in the numbers,
and press [ENTER] a few times until it gives you the factors. It even prints
them out (e.g. 2X+5) instead of just saying -.5 and such things. If you tell
it you have only one term, it acts as a way to factor a number. For some
reason, this program occasionally misses a factor. I haven't figured out why
yet; if you have, email me.

CHAP7 - POLYDIV
---------------
        This divides EX+F into AX^3+BX^2+CX+D. You see a great big
representation of the expression, and then are prompted for A, B, C, D, E,
and F. Note that if you set enter 0 for A, then this can be used to divide
a quadratic by a linear. The answers are displayed. 'r' is the remainder.

CHAP8 - KFIND
-------------
        This can find the constant ('k') for a variation function with one
or more independant variables. Simply follow the prompts. If, for example,
you are told that y varies inversely with b and directly with the square of
c, and that if b = 2 and c = 8, then y=512, you would: start KFIND, select
2:INVERSELY, give it 1 and 2, select 1:DIRECTLY, give it 2 and 8, select
3:DONE, give it 512, and -voila- be told K=16. This example makes it seem
a whole lot harder than it realy is -- I promise.

Memory Used
-----------
        Type Name                       Amt
        ---- -------------------------- ----
        prgm CHAP5                       928
             CHAP6                       643
             CHAP7                      3314
             CHAP8                       298
        list varies                   varies
        mtrx varies                   varies
        real varies                   varies
        yvar varies                   varies
                                      ------
                                      varies
All non-program items may be safely deleted with no adverse effects.

You can always find the latest version of these and all my other TI82 programs
on my website at http://sri.kbt.com/members/mlc/ti/ti.html
