Unit Q - Concept 2 - Finding All Trig Functions with Given & Identities

This SP was made in collaboration with Derik Vieyra. Please visit the other awesome posts on their blog by going here. 

Things to notice when going through the Pythagorean/Ratio/Reciprocal identities and with right triangles is that these both result in the same answers even though the methods aren't exactly the same thing. In the end both methods are used to find the ratio for their corresponding trig functions and so that is the relationship between Unit Q Concept 2 and Unit O Concept 5. It is also important to note that where the triangle lies in the quadrant determines which trig functions are positive or negative and that so always be sure to check the quadrants. Once again, thanks for checking out Derik Vierya and my blog!

SP 4 Unit J Concept 5: Partial Fraction Decomposition

 Things to look out for in this problem is that I used variables to help solve this fraction. Trying to factor things out wouldn't be possible unless using quadratic formula. You should notice that I used matrices to help cancel out variables to I can find the solutions to the answer. By using RREF on the calculator, you can find the values for each variable and also check your answer. 

Thanks for looking at this. 

SP 3 Unit I Concept 1 Exponential Functions

 This problem is to show my understanding about graphing exponential functions. It shows how to identify the x-intercept, y- intercept, domain, and range. This problem is to show when there wouldn't be an x-intercept on an exponential function and how the asymptote affects the graph. 

The viewer needs to pay special attention to why the x-intercepts do not work in this exponential function. They also need to pay attention to asymptote and how that affects the graph. The domain and range also help with the restrictions of the graph. The viewer should also see how the y-intercept is solved for. 


Steps
1. Seperate the equation into A,H,B,K 
2. Began solving for x-intercept by setting y=0 
3. Notice that it can't be done because you can't take 
the In of a negative number 
4. Head to y-intercept
5. Plug in zero for x 
6. Use pemdas to correctly solve the y-intercept. 
7. Began choosing keypoints.
8. Plug equation into calculator and look up the points
8. Write the asymptote which is also K remember y=#
9. Draw the asymptote on the graph. 
10. Write out domain and range 
11. Do it correctly. 
12. Plot points on graph. 
13. Draw a line and you're done. 

SP 2 Unit E Concept 7: Multiplicities and Graphs

This problem is to show my understanding about the multiplicities that are solved for when you factor a polynomial. It also shows the y- intercept as well as the end behavior to help others understand how I am able to graph it. The problem also shows the graph to show what the polynomial would look like if plotted on a graphing calculator. 

The viewer needs to pay special attention to the multiplicities and the end behavior. The end behavior helps tell how the end points of the graph and whether it goes up or down. The multiplicities help determine how the graph will pass the x-axis either through bouncing, going through it, or curving. These are some of the things that you, the viewer, should pay attention to when going over this problem. 

 Steps
1. Factor out the equation by splitting it up.
2. Set each factor equal to zero and solve
3. The solved are known as multiplicities
4. Multiplicities are 3M2, 4M1, and -2M1
5. End behavior show how the endpoints of the graph either go up or down. In this case they go up.
6. The y - intercept is found by plugging in 0 for all of the equations which shows that it is (0,-72)
7. The multiplicities determine how the graph passes the x-axis at the gates.
8. Roughly graph the equation according to multiplicities.

SP 1 Unit E Concept 1: Identifying The Properties of Quadratics

This problem is to show my understanding about quadratics that we learned when we watched the video podcast. The problem shows how to change it to a parent function equation as well as solving it.

The viewer should pay attention to the x intercepts as well as remembering how the axis should be labeled. They should also pay attention to the graph to see if it is plotted correctly. 

1st Picture: 

The equation I created. 

Moving the -8 to the other side.

Taking out the 2 from equation.

Completing the square to solve for missing.

Rewriting equation.

Solving for equation.

2nd Picture:

The rewritten parent function equation. 

The vertex based from the equation. 

the y-intercept by plugging in 0 for x.

The axis from the things inside parentheses.

The x-intercepts solved for in calculator.