Graphmatica Equations 101Here are some of the basic Graphmatica equations you can start with, and some notes about them. The equations are stated here exactly as you should enter them into Graphmatica.
Equation 1: y = x This is the simplest of all graphs and usually the first one we learn to draw. For variations on this graph try putting different numbers in front of the x. Variations such as y = 4x and y = 0.2x show that the steepness of the line (called the gradient) is equal to the number in front of the x. For y = x, that number is 1, being the same as y = 1x.
Equation 2: y = x^2 The equation y = x squared gives the classic parabola shape. If you turn this graph upside down ( y = -x^2 ) and shift it up a bit ( y = -x^2 + 4) you can see that it is the same shape as the path traveled by a thrown object like a ball. Physicists describe the movement of objects using variations of this equation.
Equation 3: x^2 + y^2 = 4 This equation becomes a circle when graphed. It is a quite advanced equation and is used in trigonometry for unit circle measurements of sine and cosine. The general formula for this is x^2 + y^2 = r^2 where r is the radius of the circle. Try x^2 + y^2 = 9, x^2 + y^2 = 25 and x^2 + y^2 = 100. You will see the circle radius is the square root of the number at the end of the equation.
Equation 4: y = sin (x) The sine wave is getting into some serious trigonometry and this equation is shown here just to indicate the complexity of the program. Note that for this equation the x is in brackets. Also try y = 2sin (x), y = sin (3x) and y = cos (x).
Equation 5: y = tan (x) I changed the background color so the graph would be easier to see. This equation demonstrates the effectively infinite vertical range of the plane the graphs are drawn on. Changing the graph in the same way as y = sin (x) will yield similar results.
Equation 6: y = 2^x Exponential functions can be graphed on regular grid lines or logarithmic grid lines depending on what you want to use them for. I'm pretty sure this program can also graph logs but I've not yet worked out how to do it. There seems to be no end to the Graphmatica equations that can be drawn by this program.
Going Overboard With Graphmatica Equations... Equation 7: y = x^(sin(-x)) I don't know what that equation really means, but it does serve to show one thing. Graphmatica can graph an amazing amount of points and show the detail of the graph at several different levels of zoom. The following images are that equation at successively greater zoom outs. If you look at the equation in Graphmatica you'll see that the pattern repeats at different levels, like a fractal.
You can't go wrong with Graphmatica, and the price is perfect since it's free! Return from Graphmatica Equations to Mathematics Freeware or return to the Green Planet home page for Solar Power Facts.
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