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

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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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