Graphing Cubic Polynomials

Notes

• 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) = 2x³ + 1.4x² - 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.