Section+3.1+10-13

Today in class Ms. Boca made an important announcement that she would tell Mrs. Tyson to give our class a quiz on the polynomial material we have been covering. Otherwise, we spent the rest of the time making a polynomial function graph gallery, which we did by writing a polynomial equation and then graphing it. We followed up by volunteering the most interesting graphs and then discussing what we found interesting about them.

While it might seem like it was just fun in games on Thursday, there were some important pieces of information about polynomials to be gleaned.

doesn't cross the x-axis, and so it has no noticeable, real roots, but it does have four non-real roots (listed to the right of the graph). Compare that graph and its roots with the graph (also below) of y=x^2 - 4, which has degree two, crosses the x-axis twice, and thus has no non-real roots (the roots of y=x^2 - 4 are listed next to the graph of the function).
 * We determined that the degree of a polynomial (e.g. y=x^5) determines the number of roots that polynomial has, including non-real roots. The graph (below) of y=x^4 + 10
 * We determined that polynomial graphs with an even degree (e.g. a degree of 4, 6, 8, and so on) will always increase positively towards infinity, while odd degree polynomial function graphs will not necessarily increase towards positive infinity. Look at the graphs below for proof!





Wolfram Alpha LLC. 2009. Wolfram|Alpha. http://www.wolframalpha.com/input/?i=x^4+%2B+10 (access October 13, 2011).
 * Works Cited**

Wolfram Alpha LLC. 2009. Wolfram|Alpha. http://www.wolframalpha.com/input/?i=x^2+-4 (access October 13, 2011).

Wolfram Alpha LLC. 2009. Wolfram|Alpha. http://www.wolframalpha.com/input/?i=y%3Dx^8 (access October 13, 2011).

Wolfram Alpha LLC. 2009. Wolfram|Alpha. http://www.wolframalpha.com/input/?i=y%3Dx^3 (access October 13, 2011).