Graphs of Polynomials

The sliders on the left will change the values of a, b, c, d, e, and f. The check boxes on the right will allow you to hide or show each type of polynomial so you can look at them one at a time, they also show which values will affect the graph.

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Show each polynomial one at a time and answer the following questions:
1. Change the values of the variables using the slider and observe what is happening.
2. Does the graph have any peaks? If so, how many at most, how many at least?
3. Can you make the graph not cross the x-axis?
4. What happens to the graph as x gets closer to negative infinity?
5. What happens to the graph as x gets closer to positive infinity?

T. Drew Frey, Created with GeoGebra