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

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

    You can solve this specific problem several different ways and this is one of them. In this SP we show you how to solve using identities and also using SOHCAHTOA. Make sure that you read all the side notes so you are able to understand what is going on and why we do each step. Solving using identities is trickier so make sure you look over each step as it is being done and refer back to you identities to understand why each step is happening.

SP#6 Unit K Concept 10: Writing a Repeating Decimal As a Rational Number Using Geometric Series

In this problem I am going to be showing you how to take a repeating decimal and converting it into a fraction. Make sure to pay attention to how you are plugging in your numbers into the equation. You can easily get the wrong answer if you plug it in wrong, parentheses are very important. Make sure you are also using the correct formula as well.  

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

In this problem is shows you have to partial factor decomposition with repeated factors. The first picture will go step by step with explanation to very step as why a certain step is being done. The second picture will show you have to compose it back together thus proving the first part right. Be careful with how you factor, if anything is off your entire problem will be wrong. 

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

Pay close attention to when you FOIL because the son change can really make a difference. Distribute correctly and make sure you add the As Bs and Cs in the correct place. 

SP#3 Unit I Concept 1: Graphing exponential functions and identifyingx-intercepts, y-intercepts, asymptotes, domain, range (4 points on graph minimum)

The first thing you have to do in this type of problem is figure out your a, b, h, and k, this will help you figure everything out. We know that y=k so our y will equal 9, this part of our problem is our asymptote, you should always find it first. Next thing we will find is our x-intercept. We sent y equal to 0 and this will take us back to unit H in finding how to solve for exponents, we will be using logs. In this problem you will notice that when you plug it in to the calculator it will show err. Why? Because you cannot have a negative log. This means there will be no x-intercept for this problem. We next move on to the y-intercept. You plug in 0 to the x. Here you will have to solve which is simple. Next you find the domain  which does on forever because the domain is the x-axis. Now the range is different. In the beginning we found all or our parts to the problem, now if the "a" is negative, you will have negative infinity up to the asymptote. If the "a" you will have the asymptote and then infinity. After all of this you have some points. You need more to be able to graph this so choose any point you want on the x-axis and find the y for it then graph it.

      Make sure you pay attention to how I found the x and y intercept because that will get tricky. You will need a calculator I this part to solve for it. Remember if the number it negative you will not be able to graph it.

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

     This problem is taking all that we've learned in Unit E and putting it all together. We take each concept and apply it in each step. The first step we get our equation and factor it out. The next step we find our end behavior, we do our dance to remember end behaviors. Our end behaviors helps us figure out what way the arrows will be heading in our graph. on Our 3rd step we take our zeroes from the factored equation. We take the multiplicity from them (Remember T B C(thru, bounce, curve)). Then, lastly, we find the y-intercept. We plug in 0 to all of our x's to find that.

     Pay close attention to what the multiplicity is! The multiplicity will tell you whether the line goes thru, bounces, or curves thru the x-intercepts. If its 1 it goes thru the point, if its 2 it bounces off the point, and if its 3 it curves thru the point.

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

      This problem is about creating a quadratic equation and completing the square in order to find the vertex, y-intercept, axis, and x-intercept(s).

      Make sure to pay close attention to how you complete the square to get your quadratic equation from Standard form to Parent function from.