SV#1: Unit F Concept 10- Finding all zeroes to a 4th degree polynomial

Click HERE to watch video :D

Student Video #1

        This video covers how to find all zeroes to a polynomial of 4th degree. It will start by finding all the possibilities of the coefficient and the leading degree.  Of course, there were a lot of possibilities, so we narrowed down the possibilities by using Descartes Rule of Signs. That narrowed down our possibilities and we then went straight into trial-and-error with the different zeroes using synthetic division. After bringing down the equation to a quadratic equation, we used the quadratic formula to find the remaining zeroes. We carefully solved the equation and set them x-(...) to find the exact zeroes.

        The viewer has to note that the odd degree changes signs, but that the even degree does not, just as it was mentioned in the video. Along with that, one must acknowledge that not all the possibilities work and that a only a process of trial- and-error will help lead to the quadratic equation. Also, remember that the the radical cannot be left as a negative, so there will be imaginary numbers. This goes back to the reason why we tend to count down by 2's during Descartes Rule of Sign. Lastly, the factors can be written as a quadratic equation, but it can also be left as the answer one gets after completing the quadratic formula.



*Here's a correction, sorry about the mistake.

SP#2: Unit E Concept 7- Graphing Polynomials and Identifying All Key Parts

   This concept explains the end behavior, the multiplicities that derive from zeroes, y-intercept, and a graph to represent a factored polynomial. The multiplies and the zeroes help describe the shape of the graph and the end behavior describes the limit notation used to graph the polynomial. Meanwhile the y-intercept will simply be plotted on its corresponding ordered pair. This polynomial is a positive, fourth degree function, which means that there will be a total of 4 x-intercepts, or zeroes when the reader adds the multiplicities.
          The reader needs to pay attention to the small details, such as the correct factorization since this eventually leads into our zeroes. In this case, an x^2 can be factored from the polynomial, so the reader must remember that this means that there will be two zeroes since there is a variable. Along with that, label the ordered pairs with T, B, or C because this will determine if the graph will go through, bounce, or curve; in this case, it goes through, bounces, and goes through again. Lastly, remember that the end behavior describes how the graph acts at the extreme, so make sure that the direction are correct.

                                                                                                                       

WPP #4: Unit E Concept 3- Maximizing Area

Create your own Playlist on MentorMob!

WPP #3: Unit E Concept 2: Path of Volleyball

Create your own Playlist on MentorMob!

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

Identifying x-intercepts, y-intercepts, vertex(max/min),axis of quadratics and graphing them

          This problem represents quadratic equations in standard form. This representation includes the detailed explanation of the steps included in order to identify the x-intercepts, y-intercepts, vertex
(max/min), axis of quadratics and how to graph them. We start by completing the square of the a standard form equation so we can then put in in the parent function form [f(x)= a(x-h)^2 + k]. Next, we will graph the equation by locating the vertex, the y-intercept, and up to two x-intercepts, as well as one dotted line, which will be the axis. This will result in an accurate representation of the function.
          Of course, there will be many aspects to this equation and you must make sure you notice the characteristics that must be included. For example, you must remember to complete the square correctly by first adding 2 and then factoring out the coefficient from "a". Then, you must find the parent function equation by remembering to subtract the 10 so it all equals to y. Also, one of the main points, is to notice that even though the "h" is negative, you have to get its opposite value and that the "k" remains as is. A common mistake that should not be left out is to get a positive and negative square root 5 and not just a positive value. Lastly, always check that there are at least five points in your graph before connecting the parabola's points (unless there's an imaginary x-intercept, which is not the case in this problem.
       

WPP #1 Unit A Concept 6- Linear Models

Create your own Playlist on MentorMob!

WPP #2: Unit A Concept 7- Profit, Revenue, Cost

Create your own Playlist on MentorMob!