This problem is about finding real and complex zeroes when there is a polynomial to the fourth degree. We first use Descartes Rule to find the possible number or real positive or negative zeroes. We also use the rational root theorem, p/q, to find the possible zeroes. We also use synthetic division. This video will explain how to use all these aspects to find the zeros of the fourth degree polynomial.
The viewer needs to pay special attention to Descartes Rule, when you are looking for the amount of possible negative zeroes. You have to remember that when it is an odd degree, the sign switches. The viewer also has to make sure to multiply/add/subtract correctly while doing synthetic division. The viewer has to remember that the p/q is positive AND negative. Another crucial thing that the viewer must acknowledge is distributing negatives. You must remember there could be irrational and imaginary zeroes.
Sunday, September 29, 2013
Monday, September 16, 2013
SP # 2: Unit E Concept 7: Graphing polynomials, including x-intercept, y-intercept, zeroes, (with multiplicities), end behavior.
This problem is about graphing polynomials by defining how they behave at extremas, how they behave in the middle, where their highest and lowest points are, where their intercepts are, and defining their intervals. In addition, we are dealing with multiplicity of zeroes and how it defines our graph (remember 1 is through, 2 is bounce, 3 is curve?) We will be finding the x-intercept, y-intercept, determining the end behavior, finding extrema, and noting if the graph has intervals of increase or decrease with a set equation. To make a graph efficient, we must find all these aspects.
The viewer needs to pay special attention to the end behavior and how to find it. The degree and the coefficient determines the end behavior. There is even (degree) positive (coefficient), even positive, odd negative, odd positive. The viewer needs to know which direction the end behaviors go by this. Another thing that the view has to be careful on is when they factor the equation, because it is easy to make simple mistakes. Also, the viewer has to make sure they plot their graph right and where it goes through, bounce, or curve, and apply it to the graph.
Tuesday, September 10, 2013
Monday, September 9, 2013
WPP #3 Unit E Concept 2: Finding Maximum and Minimum Values of Quadratic Applications (PATH OF FOOTBALL)
SP# 1: Unit E Concept 1: Identifying x-intercepts, y-intercepts, vertex (max,min), axis of quadratics, and graphing them
This problem is about demonstrating the process of establishing a parent function equation with a standard form to begin with. The vertex, x-intercepts, y-intercepts, and axis is to be found. To make a graph the most efficient and accurate, these steps are necessary.
The viewer needs to recognize to (x-h) in the parent function equation. The parent function equation is y=a(x-h)^2+k. To graph the x-point of the vertex, you need to know that h is opposite of what it appears to be. For example (5-2)^2. That (-2) would be 2 when you graph it. Another thing you must acknowledge is that the x-intercepts may include imaginary numbers, and when that happens you cannot graph it since it is imaginary for the x-intercepts.