Copy of Exploring Polynomial Equations

Move the sliders to observe how the graph of the polynomial changes. (Right on the graph to zoom in/out and/or to change the x/y ranges). Observe what happens to the graph as you adjust the sliders and type one interesting thing you noticed.

What happens to the graph when you make the coefficient a positive or negative?

Make a=0 and b any number but 0. What changes about the graph? What happens if b is a positive number? Negative number?

Now make a=0 and b=0, and change the values of c-g equal to anything but zero. Continue this process and record your observations. Can you make a conjecture about the graph based on the degree of the polynomial?

Change the sliders in any way (except a cannot be 0) to make as many x-intercepts as possible. What is the most you can have at once?

What are the fewest number of x-intercepts you can have?

While there may be different numbers of x-intercepts, the function still has 6 roots as long as a does not equal 0. How can this be so?