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Sunday, September 29, 2013

SV #1: Unit F Concept 10: Real Zeroes and Factorization


This problem is about how to predominantly find the real zeroes and factorization of a fourth-degree polynomial. We are given a polynomial to the fourth degree and are asked to find the possible positive and negative real zeroes as well as utilizing the Descartes Rule of Signs for it. We also must find the p/q answers in order to narrow our options in plugging in numbers for our synthetic division. Once we have a quadratic, we factor it out with mainly the quadratic formula to get our last 2 zeroes.
We must pay special attention to not make any small mistakes along the way. Any mishaps in signs or variables will result in a completely altered answer. Also, it is paramount to simplify our answers as much as possible if possible at all. As long as we follow these guidelines, then evaluating problems like these will be a breeze. Also, make sure to know the quadratic formula in order to find the last 2 zeroes.


Tuesday, September 17, 2013

SP #2 Unit E Concept 7: Graphing Polynomials

This problem covers the basics of graphing polynomials. All the essentials to graphing them include end behavior, x-intercepts with multiplicities, y-intercepts, the equation itself, the factored equation, and of course, the graph. We graphed end behavior, but that was step 1. By graphing the information in the middle, we can move on to the next level, which is precisely what this problem is all about: graphing polynomials (without increase and decrease notation as well as minimum and maximum).
There are many things to be aware of. First of all, know the multiplicities, and have the knowledge of what it means to go through a point, to bounce off a point, and to curve through a point. The names are literally what they mean. Make sure to have the write end behavior (even positive, etc.) or your graph will become incorrect. Even positive or even negative should be the focus on these student problems, and arrows should be drawn preemptively to ensure maximum clarity.

Tuesday, September 10, 2013

WPP #3 Unit E Concept 2: Nerf Bullet


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SP #1: Unit E Concept 1- Parent Function+Graph

What this picture/problem is trying to convey is how to change an equation from the standard form into the more graphable parent function form. The key terms you are trying to find are: the vertex, y-intercept, axis of symmetry, and the x-intercepts. By finding the values of all of these terms, YOU can graph more fluidly and attractively.
To gain a better understanding of this problem, one should note that the vertex is the key point of the problem. By finding the vertex, you are locating the foundation of the problem itself, thus paving your way to the values of the other key terms. To find the vertex, in the Parent Graph Equation, the x-value of the vertex is the opposite of the "h" value while the y-value is the k-value The x-intercept MAY have imaginary values, but luckily for this problem, this is not the case. Also, by utilizing the parent function form, you are attempting to create a more informative function.