Graphmatica Quick Start

Graphmatica Quick Start

About Graphmatica

Graphmatica draws mathematical graphs, like:
y = x² - 6x + 5
Graphmatica is easy to use, produces attractive results,
and is free to download: http://www.graphmatica.com .
It works well for IB Math Portfolio work.

Below is a quick-start introduction to Graphmatica.
(The pictures are smaller than you will normally see.)

Starting

When you start Graphmatica the first time, you might not like the layout -
funny colors, small numbers.

Change Scale

Change the numbers (scale) with View/Grid Range

Better Colors

Choose better colors with Options/Graph Paper/ Colors (choose White):

Draw First Graph

Now you will have white paper with colored lines, and you can draw your first graph.
In the formula-box, type : y = x^2 + 2x - 4
(The ^ symbol stands for power, so x^2 means x² .

Monochrome

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.

Draw Another Graph

To add another graph, type the formula in the formula box and press [Enter].

Tracing Coordinates

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.

Zoom

There are two ways to zoom in and out :
- View/Grid Range - change the grid-range by typing limits for x and y
- Mark and Zoom - hi-light 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 .

Marking Points

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 data-table again but the dots will stay.

Adding Labels (annotations)

You can label points or add other annotations (notes) to your graph.
Use Edit/Annotations. If you want to move the annotation later,
double-click on it, click the [Place] button, then click on the graph
to place that annotation.

Best Fit Line

You can plot data points and ask Graphmatica to find the best-fit-line.
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 best-fit-line 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.

Copying the Picture

Use Edit/Copy (BMP) to copy your graph. Then you can paste it into a document.
Copy using EMF might work better for some word-processors, but BMP probably
works for most normal applications.

Before copying, you might want to
resize the Graphmatica window, as resizing in a word-processor might make the picture ugly.

Saving your Work

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.

Erasing

There are two ways to erase a graph. Right-click on the graph then choose:
- hide - makes the graph disappear, but keeps the formula
- delete - makes the graph disappear and throws away the formula.

Summary of Symbols

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*	x²	x^3
*Square Roots*		sqrt(x)
*Cube Root\*		x^(1/3)
*Fractions*	¾	(3/4) (x+1)/(2x) ( use parentheses ! )
*Degrees*	sin x^o	sin(x*d)
*Domain*		sin(x) {3,9}
*Absolute Value*		abs(x-2)
*Inequality*		y <= x + 3
*Pi = 3.141..*		pi
*e = 2.718..*	e	e
*Trigonometry*		sin(2x)
*Inverse Trig*		asin(0.5)

Advanced Functions (Calculus)

Graphmatica contains some advanced features for investigating graphs.

Roots (Zeroes)

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.

Slope (Tangent Line)

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.

Derivative

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).

Integral (Area)

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> ).