Dynamically-Generated Polynomial Function Examples Start with these examples and explore variations on the results: Discover what polynomial functions are all about Linear (1st Degree) Increasing Function The red color indicates that the graph is increasing. If you move your cursor over the image, you will see the graph change color to black, which indicates the absence of concavity. The graph is neither concave up nor concave down. Linear (1st Degree) Decreasing Function The blue color indicates that the graph is decreasing. Parabolic (2nd Degree) Opens Up Red highlights the curve segments where the graph is increasing; blue highlights the curve segments where the graph is decreasing. If you move your cursor over the image, the graph changes to purple, which indicates that the graph is concave up. Parabolic (2nd Degree) Opens Down If you move your cursor over the image, the graph changes to green, which indicates that the graph is concave down. Cubic (3rd Degree) Two Turning Points If you move your cursor over the image, the graph changes to both purple and green: purple highlights the curve segments where the graph is concave up while green highlights the curve segments where the graph is concave down. Cubic (3rd Degree) No Turning Points Cubic See why the automatically determined viewing window makes graphing easy. In this window, the ratio of the height to width unit lengths is greater than 1000 to 1. Quartic (4th Degree) Three Turning Points Color coding curve segments helps to distinguish increasing/decreasing curve segments and concave up/concave down curve segments. Quartic (4th Degree) One Turning Point Quintic (5th Degree) Two Turning Points (& Three Points of Inflection) Quintic (5th Degree); See How Color Coding Predicts "Hidden" Features Use Smart Zooming with, say, Xmin=–3 and Xmax=3 and click the GraphAgain button to reveal "hidden" turning points and changes in concavity. 8th Degree 17th Degree This example illustrates the need for a properly sized window. On WebGraphing.com, the automatically determined window includes all the important mathematical features.

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