SP#7: Unit Q Concept 2: Finding All Trig Functions When Given One Trig fFunction and Quadrant

Please see my SP7, made in collaboration with Elizabeth T., by visiting their blog here.  Also be sure to check out the other awesome posts on their blog

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

     The viewer needs to pay attention to finding the ratio by dividing the second term by the first. Additionally, when dividing the numerator by a fraction, multiply the top and bottom by its reciprocal. It is crucial to remember the whole number 2 at the beginning of the problem. Add it to the solution by multiplying top and bottom by 99 to get the same denominator and then add the two.

SP # 5 Unit J Concept 6: Partial Fraction Decomposition with Fractions



     Please pay special attention to how  I got a, b& c. Look closely to how I checked my answer. How I got  my matrices. As well as where I got my equations and how i got the same denominator but different numerator. And what I did after. 
    

SP #4 - Unit J Concept 5: Partial Fraction Decomposition with distinct factors

 

 

 

 



     For the first picture 1,special attention should be payed to multiplying out the numerator. Also, be careful when distributing negative numbers, you must distribute the negative to everything in the parentheses, then combine like terms. For the second picture the viewer should be careful when writing the equations. It is important to copy correctly and not forget any negative signs. It is also crucial the viewer remembers to cancel out the x's.
      For the third picture plug in the coefficients into the calculator. It is crucial you plug in the right numbers or else you will get the wrong answer. It is important to recheck what you plugged in. Follow the necessary steps to find the ordered triple. The viewer should be able to follow the steps as stated in the image. It is important not to forget the closing parentheses! The fourth column provides the ordered triple, notice that these are the numerators of the original equation found in part 1.

SP #3 Unit I Concept 1:Graphing Exponential Functions

 

The viewer needs to pay close attention to solving or the x-intercept. We cannot take the log of a negative number, so if this occurs, it is undefined, meaning no x-intercept. Additionally, it is important to notice that the range depends on the asymptote. If you look at the graph, you can see that the graph never goes below  and goes up to infinity. Also when choosing key points, the 3rd key point should be h.

 



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

 

 

           This problem is graphing a polynomial function when given a set of zeros. In this case, the zeros given were 2 M2,4M1, 1M1. From there, you have to find the end behavior and y-intercept. Finally, with the help of a graphing calculator, (if wanted) will help you find an accurate graph.

      There are several things to pay attention to when following this program.  The amount of zeros automatically tells us which degree this polynomial will be in (the 4th). Another thing to look out for is to pay attention to the zeros first because that is what were starting with.

        

 

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

   You are trying to find the vertex, x-intercepts, y-intercept, and the axis of symmetry.This problem is about changing an equation from standard from into parent function form so that it is easier to graph. Multiple steps are necessary to finding the solution. These steps will ultimately make graphing the equation easier and more accurate.
       In order to understand, special attention should be given to finding the vertex. We must remember that h is the opposite of its sign in the parent function. Additionally, it is necessary to recall that the x-intercepts may have 1, 2 or none (imaginary) x-intercepts. Also, to better understand, we must also recognize that the parent function allows us to show an accurate representation of the function.