WPP #9: Unit L Concept 4-8 - FCP, Combinations, and Permutations

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SP 6: Unit K: Concept 10: Writing a repeating decimal as a rationalnumber using geometric series

While doing these types of problems, the solver has to pay attention to details. When finding "a" sub "1" and "r", you have to make sure that you are using the proper decimal places and fractions. Also, you must make sure to plug in the information to the formula correctly, by misplacing a number, you could throw off the answer. Lastly, make sure that you are multiplying, adding, and dividing the numbers correctly 

Fibonacci Haiku: Alexis

http://25.media.tumblr.com/f511c86d5ec0873aa23fccf8c95656ab/tumblr_min5dlnixh1r4xjo2o1_500.gif

Alexis
Derpy
The homie
One hungry girl
A lover of pussy cats
Food and boys are her life long passion

SP 5: Unit J Concept 6: Partial Fraction Decomposition with Repeated Factors

The viewer needs to pay attention to a few things throughout the problem. The first is that they count up when creating "A, B, and C!" Also, they must combine the like terms correctly and properly distribute the variables. Lastly, when finding common denominators, they viewer must make sure that they are multiplying by the right factors! Good luck!

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SP #4: Unit J Concept 5: Partial Fraction Decomposition with Distinct Factors

While doing these types of problems, the viewer has to pay attention to detail! Mixing up positives and negative can affect the entire problem! Also, when finding common denominators, the viewer needs to make sure that they FOIL the factors correctly.Lastly, when choosing  variables, you must avoid "X" because it already plays a role in the problem! Thanks for viewing and good luck. 

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SV5: Unit J Concepts 3-4: solving three-variable systems using Gauss-Jordan elimination/matrices/row-echelon form/back-substitution and solving non square systems

to watch my video, please click HERE

Some of the most important things that the solver needs to pay attention to are the positive and negative signs! One mistake can throw off the entire problem. Also, they should make it a point to keep track of what they are doing to each row by writing it down on the line next to it. One of the last things they should make sure to pay attention to is that when back substituting, they do not mic up the value or place them in the wrong order(in the ordered triple)

WPP# 6: Unit I Concept 3-5: Compound Interest, continuously compounding interest, investment application problem

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SV #4: Unit I Concept 2 - Graphing logarithmic functions and identifying x-intercepts, y-intercepts, asymptote, domain, range (4 points on graph minimum)

To watch my video, please click HERE

The viewer needs to pay special attention to a few things throughout this problem. The asymptote is something that the viewer needs to pay attention to. They need to make sure that they change the sign of the h value in order to match the formula. Also, they have to exponentiate correctly in order to find the x-intercept. While finding the y-intercept, you have to make sure that the change of base formula is set up correctly in order to receive the correct value. The domain is also important as it has to be set correctly in order to make the graph correct.

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SP #3: Unit I Concept 1 - Graphing exponential functions and identifying x-intercept, y-intercept, asymptotes, domain, range (four points on graph minimum)

In this type of problem, the viewer needs to pay special attention to the parts of the exponential equation (y = a x b^(x-h) + k). "A" will tell you if the graph is going to be above or below the asymptote and "k" will tell you where the asymptote is.  These are the two most important values of the equation. You have to make sure that your asymptote is horizontal for these types of equations. You find the Key Points by inputting the equation into the "y=__" screen then looking at the table. Also, solving for the x and y intercepts need to be accurate in order to make the graph more precise. Domain will always be (-inf., inf) as there is no x asymptote. The range depends on the asymptote. If your graph is neg., then the value goes to the y slot as it is below the asymptote. If it is a positive, then it goes into the x slot as it allows the line to be on top of the asymptote.

SV#3: Unit H Concept 7 - Finding Logs Given Approximations

To watch my video, please click HERE

In order to fully understand these types of problems, the viewer needs to pay special attention to the properties. For example, if a clue has an exponent, then the solver needs to know that the power property transfers the exponent to the front of the log. The product and quotient laws are very important for the reader. These laws will tells the problem solver whether they will need to add or subtract the clue throughout the final answer. Also, the viewer needs to notice that logb of b=1. This will provide them with extra clues to find their treasure!

SV#2: Unit G Concepts 1-7 - Finding all parts and graphing a rational function

To view my video, please click HERE 

This problem is about finding the horizontal, slant, and vertical asymptotes, holes, domain in interval notation, x and y intercepts of rational functions, and graphing functions with all parts. The first step to this equation is noticing that the numerator has a greater degree than the denominator. This means that we go on to find the slant asymptote by using long division. We stop once you receive a y=mx+b equation. Next you find vertical asymptotes. This requires factoring and cancelling out any common factors from the polynomial. You set the remaining factors equal to 0 and solve. This number is your vertical asymptote value which is then used in limit notation. Next, you use the cancelled factors and set them equal to zero to find any holes in the graph. The domain comes fro the vertical asymptote value and is then used in interval notation to decide the direction of the graph. You find the x-intercepts by setting the simplified numerator equal to zero and solving for the x's. The y-intercepts are found by replacing the x's of the polynomial with zeroes.Then you graph the polynomial!

Some things that the problem solver needs to pay attention to are that they respond properly to the degrees! For example, in this problem, there was no horizontal asymptote because the degree of the numerator was larger than that of the denominator. Also, they have to factor correctly so that they can properly find the vertical asymptotes, domain, and holes! Lastly, they have to make sure that their graph does not touch the asymptotes of the graph. 

SV#1: Unit F Concept 10 - Finding all real and imaginary zeroes of a polynomial

To view my video, please click on the link HERE.

This problem goes over finding real and complex zeroes if you are given a 4th or 5th degree polynomial. In this case, we are given a 4th degree polynomial. The first thing that needs to be done in order to find the zeroes of the polynomial is to use the rational roots theorem. You find the factors of p and q and use the equation p/q to find the possible rational zeroes. Next you use Descartes rule of signs to find the possible number or real zeroes (positive or negative). Then you put the possible rational zeroes to work by using them as the divisors in synthetic division as you divide the polynomial. You use synthetic division to decrease the power of the polynomial to a quadratic. From there, you use the quadratic formula to find the remaining zeroes. 

There are some things that you need to pay special attention to. The first thing that you have to pay attention to is that you place the p's over the q's, not the q's over the p's! Also, when using Descartes rule of signs, it's important that you flip the odd powered exponents in order to find the correct number of possible real zeroes. Also, throughout the process of the equation, you have to be careful that you are multiplying, dividing, adding, and subtracting correctly, as those little mistakes can make a huge difference in the final answer. 

^FINAL ZEROES^

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SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

This concept has to do primarily with graphing polynomials by using zeroes and mathematic laws. You first factor the given polynomial to make it easier to deal with! It is important that you COMPLETELY factor the polynomial. By completely factoring the polynomial, it is easier for the problem solvers to find the zeroes of the graph. The next step is to define the end behavior. This is done by looking at the leading coefficient and the exponent attached to it. In this case the leading coefficient is positive and the exponent is even so it is an even positive graph. After this is completed, use notation to tell the viewers in which directions the lines will go. Then, find the zeroes by setting the factors equal to zero and solving. If there are multiples of an answer, use the word "multiplicity" and the number of times that the value is repeated. Then plot the points and graph while using TBC 123!

It is very important that you factor the polynomial completely and correctly. One small mistake in the early process could cause a big change in the final graph. Also, make sure that the end behavior is correct. After all, you want to go through the doors not run through the wall. Don't forget, TBC, 123!

SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

A quadratic has four main parts: the vertex (max/min), x-intercepts, y-intercepts, and an axis of symmetry. Each part plays a key role in the creating and understanding of a parabolic graph. By taking an equation in standard form and manipulating it into a more easily graphed parent function, problem solvers are able to retrieve important information. 

The problem solver does have to pay attention to the details in order to be sure that their work is correct! For example, it is essential that the parent function follow the correct form: f(x) = a(x-h)^2+k. Once the problem is correctly converted into the parent function form, they can easily withdraw information from it. The vertex (h,k), x-intercepts (y=0), the y-intercept (x=0), and the axis of symmetry (x=h)! With these simple equations, the problem solver is on their way to a great graph! What they must remember is that the work has to be transferred correctly! 

Explain

You are given the problem: f(x) = 4x^2+24x-2. The first step is to add a 2 to both sides. Next, you factor out the constant from the leading value out of both the first and second term (don't forget to add it to the other side as well!). To find the missing term, use the formula "b/2^2". You then fill in the answer into the two blanks. Finally you simplify it to make it into the parent graph equation! Lastly, use the given formulas to discover the vertex, y-intercept, x-intercepts, and axis of symmetry. 

WPP#4: Unit E Concept 3 - Maximizing Area

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WPP#3: Unit E Concept 2 - Path of Football (or other object)

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

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WPP#1: Unit A Concept 6 - Linear Models

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