SP#7: Unit Q Concept 2: Finding all trig functions when given one trig function and quadrant (using identities)

"This SP#7 was made in collaboration with Tracey P. Please visit the other awesome posts on their blog by going here."

Now, there is more than one way to find our answers and solve for the function, two are those that will be expressed throughout this post. We know that we can solve this using identities or by using SOH CAH TOA! So, the following pictures will display the solutions to the problems in both ways and using both methods. (: In the end we will find out how you get the same answers either way!

The first image will show and go over how to solve this function when using identities.

This second image will go over solving the function by using the wonderful SOH CAH TOA!  

In order to be able and understand this problem and be able to deal with it as you solve it, you have to be able to know the different types of identities and they should be able to mix and match and substitute several terms for others. Also, of course you have to know what SOH CAH TOA is and the ratios for each. Also, you should be familiar with all of the ratios and how there could be more than one. It can be difficult, but with practice everything will be fine. (:  

SP #6: Unit K Concept 10

Although these types of problems seem the easiest, they can become the trickiest of all due to the fact that there are several phases of which you can make silly mistakes. It is important to pay attention when it comes to knowing how many zeros go after the decimal and also when it comes to the dividing since they are fractions. You have to remember to multiply by the reciprocal and then another important part is making sure whether there is a number in front of the decimal like in this case. Remember to add it in the end and do not just forget like I almost did.

SP #5 Unit J Concept 6

SP #5 (: 

While solving this problem, it is similar to the other and you have to be cautious when it comes to the foiling and the distributing as well. Also, do not forget to get rid of the x's when towards the end because if not you will not be able to continue solving. Be sure to solve properly and then use RREF to solve fully. Plug in the numbers correctly and make sure to know how to use the different buttons and the next steps. 

SP #4: Unit J Concept 5

SP #4 :) 

When solving this equation it is important to be careful when foiling and distributing properly while searching for the common denominator. Also, since there are several steps to the problem you should just be aware of what you are doing and the steps that come next. When combining like terms it can get confusing so it is best to do it all out in paper and carefully. Lastly, know how to use the calculator and be sure to plug in the numbers correctly. 

SP # 3: Unit I Concept 1

The equation is:
F(x)= -2(2)^(x+2)-1

For this problem, the first step that we would do is identify a-k and then the asymptote becomes easy (y=k). Then, finding the x and y intercepts would come and we would do so by plugging y as zero when solving for the x intercept and then plugging in zero for x to find the y intercept. The domain and range you can either do before or after graphing the equation. Plug in any key points, just make sure that the third one is your value of h to make it easy. Plot the points and then you are basically done. 












What does the viewer need to pay special attention to in order to understand?
While solving the problem the viewer should pay special attention to the original equation and whether a indicates it as below or above the asymptote. This will come in handy for the graphing as well. Now, if and when you get a negative natural log then you have to realize and remember that it means it will be undefined. Remember that the domain is always all real numbers and then since in this case for the range it is below that means that you will start from negative infinity up to the asymptote. 

SP #2 Unit E Concept 7: Graphing Polynomials

SP

      What is this problem about?                                                                                                                                

             This problem is basically about graphing a polynomial and being able to find several factors to it. For example,  from the equation we have to factor it out and then find the zeros, or x-intercepts. Some times you can start off backwards, like in this case, by coming up with the zeros first and then the factored equation to finally foil. Finding the y-intercepts as well would a task and then the extrema with the intervals of increase and decrease. To be able and graph it, you look at the zeros and decide whether the graph will go through the point, bounce, or curve. The way you decide is by knowing what the multiplicities are. 

What does the viewer need to pay special attention to in order to understand? 
            The viewer needs to pay special attention to the x-intercepts and know what the multiplicities exactly due to the fact that the graph will come out incorrect if the multiplicities are wrong. Also, another thing is that knowing the end behavior is important since it will give you a hint of how the graph will look like. Just overall be cautious because one simple mistake can ruin the whole problem. 

SP #1 Unit E Concept 1: Identifying Parts of the Graph of a Quadratic

SP 

1. What is this problem about? 
     This problem is about parent graphs and being able to graph them as well as find many different factors of the quadratic. For example, we are going to be finding the y-intercepts and x-intercepts algebraically. Also, finding the vertex is another point to this problem. We will be able and get to all of those answers by completing the square of the function.


2. What does the viewer need to pay special attention to in order to understand? 
     The viewer needs to pay special attention to the way that the parent function equation is written. The reason is because they have to make sure and it is not written in standard form. Another thing is that they have to be extra careful and be cautious when it comes to imaginary numbers.