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Sunday, September 29, 2013

SV #1: Unit F Concept 10 - Finding All Real and Imaginary Zeroes of A Polynomial


        This problem concerns deriving zeroes from given polynomials of either the 4th or 5th degree. Basically, you work out the problem until you arrive at an end result of 4 zeroes (for 4th degree polynomials), or 5 zeroes (for 5th degree polynomials). In doing so, however, there are several crucial steps that must be taken in order to ensure the success of your efforts. Anyways, this could be useful in graphing, too.
       Some important things that one must pay attention about in order to master this concept include remembering to use the rational roots theorem, and the Descartes Rule of Signs, and remembering to put zeroes in to fill voids when an x is missing in the polynomial. The most important thing, however, is to remember that you may more easily complete this process by utilizing a graphing calculator in order to identify zero heroes. But, as scholars, is it not more honorable to walk the path filled with thorns in order to ensure our complete mastery of this concept? Either way, yeah; it is easier to use the graphing calculator.

Monday, September 16, 2013

SP #2: Unit E Concept 7 - Graphing A Polynomial And Identifying All Key Parts

        The purpose of this problem is to derive a polynomial function from a designated number of zeros and a designated power and coefficient. With this in mind, we graph a fourth degree polynomial with an even coefficient for its highest x-power, all without of the complications that a graphing calculator obviously presents. This is done by first extracting the factors from the polynomial, or formulating them from the zeros that were given, and then deciding the orientation of the ends of the graph. That is all.
        Some important facts to factor in are to pay attention to the: orientation, through / bounce / curve x-intercepts, and whether or not it looks right. An important thing that must be done (that is excluded from this problem) in order to graph a more accurate graph, is to try and figure out the extrema of the graph. Don't forget to utilize that, and of course, the y-intercept in more accurately displaying your graph. An extra thing that could be done would be to check whether or not your graph is correct on a graphing calculator. Don't forget to input the correct things though, for your calculator is only as smart as you.

Wednesday, September 11, 2013

Tuesday, September 10, 2013

Monday, September 9, 2013

SP #1: Unit E Concept 1 - Graphing A Quadratic and Identifying All Key Parts


        This problem is about deriving a parent function type equation from a regular trinomials, so that graphing the equation wouldn't be as hard as it would have been had you tried to graph the other way. Basically, it's about finding the values that we deem crucial in graphing polynomials, which include the vertex, x-intercept(s) (if there are any), the y-intercept (if there is one), and the axis of symmetry. Ultimately, it's about going through this infinitude of steps, and arriving at a simpler means.
        I think that the reader needs most, to pay special attention to whether or not my writing is intelligible to them or not. However, in all seriousness, though, I think that they need to know that all of the important values that we need, can be calculated simply on a calculator right from the start, without having to go through any of these steps. To each, their own, I guess. Also, it's pretty important that you realize imaginary numbers cannot be graphed regularly, such as regular x-values, on a regular graph.

Tuesday, September 3, 2013