-- A polynomial equation can be specified in the url by passing the coefficients (a) as a reversed, comma delimited sequence. For example: the equation:

*y = x ^{2} + 2 x - 3*

Is referenced as:

```
graphs.html?a=-3,2,1
```

-- A series of points can be entered as a comma separated list of x, y coordinates. For example, the points:

*(3,7), (2,-3), and (5,1)*

Can be plotted as:

```
graphs.html?pts=3,7,2,-3,5,1
```

*none* - Turn off the input boxes at the top of the graph:

*polynomial* - (default) Show the interface for polynomial equations.

*points* - Show the interface for adding points to the graph.

For example, the url for the above equation with no input box would be:

```
graphs.html?a=-3,2,1&show_input=none
```

*auto* - (default) scales so graph is slightly smaller than window so there are no scroll bars on the frame.

*full* - scales so graph is fully fits the smallest dimension of the iframe window.

*none* - creates 600x600 pixel graph in a window.

For example, the url for the above equation with no input box and full fit:

```
graphs.html?a=-3,2,1&show_input=0&fit=full
```

-- The default range is *10* so the x and y axes minimums are *-10* and the maximums are *10* (as shown above). By default, the tick marks are interpolated to be 10% of the range. To change the range to 20 use:

*range=20*

So, for example:

```
graphs.html?a=-3,2,1&range=20
```

-- The default tick marks are interpolated to be 10% of the range if the width of the graph is greater than 300 pixels, and 20% if smaller (note that these do not exactly correspond to the values set for the iframe since, except for the *fit=none* option, some adjustment is made. To change the dx to 5 use:

*dx=5*

So, for example (with the range set to 20):

```
graphs.html?a=-3,2,1&range=20&dx=5
```

-- Enter a comma delimited list of:

*a*- the left bound (lower limit) of the area.*b*- the right bound (upper limit) of the area.*n*- the number of trapezoids used in the integration.

So, to find the integral (area under the curve) between *x = 1* and *x = 5* using 4 trapezoids use:

*integrate=1,5,4*

For an example, we'll find this integral for the curve *f(x) = -0.25x ^{2} + x + 4 *:

```
graphs.html?a=4,1,-0.25&integrate=1,5,4
```

The area using 4 trapezoids is 17.5 as shown in this numerical integration example.

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Graphing Polynomials by Lensyl Urbano is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Based on a work at earthsciweb.org.

Based on a work at earthsciweb.org.