Graphmatica draws mathematical graphs, like: Below is a quickstart introduction to Graphmatica. 
When you start Graphmatica the first time, you
might not like the layout 
funny colors, small numbers.
Change the numbers (scale) with View/Grid Range
Choose better colors with Options/Graph Paper/ Colors (choose White):
Now you will have white paper with
colored lines, and you can draw your first graph.
In the
formulabox, type : y = x^2 + 2x  4
(The ^
symbol stands for power, so x^2 means x^{2}
.
If you don't like the purple color for
the graph, you can change it in Options/Graph Paper/Colors.
Either
change the colors of Graph1, Graph2, etc all to black, or change to
Monochrome layout.
To add another graph, type the formula in the formula box and press [Enter].
Find the coordinates of the point of intersection by
moving the cursor to that point
(trace the graph), and then read the coordinates
at the bottom of the screen.
There are two ways to zoom in and out :
 View/Grid Range  change
the gridrange by typing limits for x and y
 Mark and Zoom 
hilight an area then click the zoom buttond
Use the Default Grid button
to return to the normal view.

Automatically Find Intersection
Use Tools/Find Intersection to automatically find the points of intersection.
This
gives better results than tracing, as tracing only finds approximate coordinates

e.g. 1.995 instead of 2.0 .
You can mark points on the graph  for example, the points of intersection

by using View/Data Plot Editor. Type the coordinates of the
points
you want to mark with dots.
This will squash your graph to make room for the data table.
After typing
the points, you can hide the datatable again but the dots will stay.
You can label points or add other annotations (notes) to your graph.
Use
Edit/Annotations. If you want to move the annotation later,
doubleclick
on it, click the [Place] button, then click on the graph
to place that annotation.
You can plot data points and ask Graphmatica to find the bestfitline.
Open
View / Data Plot Editor and type in your data. Then click [Options],
then
[Curve Fit], select Polynomial, and change Maximum Order to [1].
This forces
the [Curve Fit] button to use a straight line to fit the points.
The equation
of th bestfitline appears at the bottom of the screen.
Implicit Functions  Relations
Graphmatica will also graph relations (implicit functions), such as circles
and conic sections.
You can also graph a line from an equation, without solving
for y. You can also graph
inequalities and it will shade in
areas for you.
Use Edit/Copy (BMP) to copy your graph. Then you can paste
it into a document.
Copy using EMF might work better for some wordprocessors,
but BMP probably
works for most normal applications.
Before copying, you might want to 

Use File/Safe or Save as to save your graphs. You might also
want to use
File/Save Setup Info to save your color and size settings,
so these will stay
the same for new graphs.
Be aware that this doesn't actually save your picture, but rather
saves
all the formulae you wrote. If you drew lots of graphs
and erased them,
they will all appear again when you open the file
next time.
There are two ways to erase a graph. Rightclick on the graph then
choose:
 hide  makes the graph disappear, but keeps the formula

delete
 makes the graph disappear and throws away the formula.
You must use Graphmatica notation to define
functions, but do not use this notation
when writing
mathematics in an IB Portfolio. Here is a summary of common symbols.
More
details available in Graphmatica Help / Graphing Equations / Operator Table.

Normal math 
Graphmatica 
Multiply 
3·5 
3*5 
Divide 

x / 4 
Powers 
x^{2} 
x^3 
Square Roots 
sqrt(x) 

Cube Root\ 
x^(1/3) 

Fractions 
¾ 
(3/4) 
Degrees 
sin x^{o} 
sin(x*d) 
Domain 

sin(x) {3,9} 
Absolute Value 
abs(x2) 

Inequality 
y <= x + 3 

Pi = 3.141.. 
pi 

e = 2.718.. 
e 
e 
Trigonometry 
sin(2x) 

Inverse Trig 
asin(0.5) 
Graphmatica contains some advanced features for investigating graphs.
Click on the curve you want to investigate. Then use Calculus /Find
Critical Points
to find the zeroes (roots) of the function. For
the parabola, this also finds the vertex.
Use Calculus/Draw Tangent Line to find the slope of a curve at a point.
Click
on Draw Tangent Line, then click on a point on the curve.
Use Calculus / Derivative to find the derivative of a function  this
will also
draw a graph of the derivative. If you don't want to see
the graph, hide it.
Click on the graph of the derivative to see it's formula
(at the bottom).
Use Calculus / Integral to calculate an integral  this calculates
the value of the area
as a number  it will not give a formula as
an answer. You can find the area between
to functions, or just the
area under a function (change the second equation to <none> ).