## Graphing Cubic Polynomials

Graph

- Change the numbers in the boxes to change the coefficients
of the polynomial. The default values
are 2, 1.4, -1.2, 0, corresponding to the polynomial
f(x) = 2x^{3} + 1.4x^{2} - 0.8x

Small numbers --- between, say -2 and 2 ---
will work fairly well. With larger numbers you will have to
"zoom out." Press "Redraw" after you
change the coefficients.

- Click on a point in the plane to determine its coordinates.
Use this to find approximate values for the zeroes of the
polynomial. There are three zeroes; you may have
to zoom out to find them all.

- "Zoom in" magnifies the graph
and "zoom out" reduces it. The origin
stays fixed while zooming. Try repeatedly zooming
in. The displayed curve will approach a segment of
the tangent line at the origin:
limit( magnified curve ) = tangent line

- The rise/run of the curve from left is displayed.
This quantity will approach the slope of the tangent
line as you zoom in:
limit( rise/run ) = slope of tangent line

- The approximate arc length of the curve is
displayed. This is computed by approximating
the curve by 100 line segments, then adding up
their lengths.

- The default interval for displaying the graph
is [-1, 1]. This can be changed in the HTML file
for this web page. Likewise the default coefficients
are displayed in the HTML file. Thus one applet
can be used for many examples.

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Last modified by jac at 14:03 on 12/21/1997.