Complex Numbers

On Friday we began talking about complex numbers. Be sure that you have completed the assigned problems before class on Monday. You will recieve your Quadratic word problems on Tuesday, to complete over the break.

Coming up:
- Complex numbers this week.

Posting for Points:
Who had a sibling in the talent show friday?

Long Division and Synthetic Divsion

Today we talked about the uses of Long Division and Synthetic Division and the process for each. Remember that we use these methods to find the roots of any polynomial beyond a quadratic! We will carry this process into our discussin of complex (imaginary) numbers at the end of the week.

Coming up:
- Homework is from section 2.3

Posting for Points:
How many roots do you expect to find from a quartic equation?

Factoring

Today we spent some time reviewing different methods of factoring. You need to be extremely comfortable with factoring by Friday! Extra practice can be found on page 149.

Tomorrow we will talk about factoring polynomials beyond quadratics.

Coming up:
- Homework: pg. 149 #'s 35-40

Posting for Points:
What does the solution to a quadratic tell us about the graph?

Test Tomorrow

You will have a test tomorrow on Quadratic Modeling. The test will include all topics that we discussed in class. Do not forget the extra problems that I recommended to you. Study hard!!!


Coming up:
-Test Tomorrow!!!!

Posting for Points:
Does Wile E Coyote ever catch the Roadrunner?

Quadratic Review

Today we continued reviewing quadratics. You should have completed the Wile E Coyote problem in class or for homework.

Coming up:
- Test Friday!!

Posting for Points:
Free posting point tonight!

Polynomials and Quadratic Review

Today we talked about Polynomials and their graphs. Thus far you only know how to solve a polynomial if it can be manipulated to a quadratic. We will not look at other methods for finding these roots until after our test Friday.

The test this Friday will include only our Quadratic information (Solving for "a", using matrices, word problems, and finding the roots). We will review tomorrow and Thursday.

Have a great week!

Coming up:
- Test Friday!!!!!
- Tomorrow we will review

Posting for Points:
How was your class trip?

Friday and Posts this Week

On Friday you guys became engineers for the day. You had to create a scale drawing of your quadratic creation, and then find the equation representing your model. There were some very creative creations and everyone found their equivalent "a" values using both methods of solving.

This week there will be no posts due to class trips. Everyone have a safe and fun time!!

Have a great time on class trips!

Coming up:
- We will look at more polynomials when we get back.
- Your grades are up so be sure to check those if you have not seen them already

Posting for Points:
Free posting points all week!

St. Louis Arch

The St. Louis Arch equation has been found. First we found the equation using our original method discussed in class yesterday (using the vertex to find the standard equation, and then solving for "a"). Then we introduced using Matrices to solve a quadratic equation. This was a brief introduction to Matrices, as we will spend an entire chapter on them next semester, but it is important that you see how useful they can be for solving Systems of equations and Quadratics.

If you were not in class you should visit the website on the right to see the steps in solving a Matrix.

We also analyzed these two equations (one from each method), and discussed the importance of "a" in the equation, and why the vertex is almost irrelevant! It all depends on exactly how you set up the graph, but you will always have the same parabola, as long as your "a" is the same. The other numbers just give you the transformations!!!

Have a great time at the Fall Festival!!!

Coming up:

- If you were not in class you should complete this worksheet (just numbers 1-6)

- Tomorrow we will use these same techniques to find another famous arch!!

Posting for Points:

Can you think of another famous arch? (Think fast food)

St. Louis Arch

Today we talked about quadratics some more, and specifically focused on how to find the equation if given only the graph. You should now be able to also apply these concepts to a word problem.

Tonight for homework you must determine the equation (a quadratic) representing the St. Louis Arch using the picture provided in class. Use our word problems from class to help you set up the equation.

Have a great night!

Coming up:
- Homework: Find the equation representing the St. Louis Arch
- We will begin looking at matrices tomorrow

Posting for Points:
Where is the St. Louis Arch?

Quadratic (x-intercepts)

Today we finished talking about quadratics, specifically about how they move, and how to find the equation using two points from a graph. If you were not in class you definitely need to get some notes from someone, but you can check out the examples on pages 131-134. We focused on finding the x-intercepts and solving for "a" in the equation f(x)= a (x-h)^2 + k.

Let me know if you are still confused (when you post your comment) and I will post some examples tonight.

Have a great week!

Coming up:
- HW pg. 135 #'s 36-42 even, 78, 79, and find the x-intercepts from last nights homework (14-24)
- Tomorrow we will look at using Matricies to solve quadratics

Posting for Points:
From the standard equation of a quadratic, what do h and k tell you?

Standard Quadratic

Today we focused on the specifics of a Quadratic function. We talked about both the "normal" equation and the standard equation. Be sure that you know how to use each, and how to change from one type to the other. You should also know what the vertex and the axis of symmetry are in a quadratic function. If you missed the notes today get them from someone ASAP.

Have a great week!

Coming up:
- Homework p. 134 #'s 9, 14-26 even

Posting for Points:
What is the equation for finding the axis of symmetry?

Midterm Grades

Today I returned your midterms. We spent part of class going over the answers and correcting them. Be sure you understand all of these concepts.

Have a great weekend!

Coming up:
- We will start looking specifically at quadratics on Monday

Posting for Points:
What is the UNC mascot?

Study for Midterm

Study for your MIDTERM!!!! Good Luck!!! Study Hard!!

Coming up:
- Midterm Tomorrow!!

Posting for Points:
Enjoy a free posting point!! (tell me how excited you are if you want)

Midterm Review

Today we went over the homework from Monday and reviewed for the Midterm. Be sure that you are studying your old tests and correcting any mistakes you made.

Coming up:
- Midterm this THURSDAY!!! We have moved it from the original date (Friday).

Posting for Points:
When is your Midterm now? (sorry for the date changes but this should benefit everyone)

Problem Solving

We started today by reviewing the problems you had for homework dealing with the different types of variation. Be sure you know how to find the regression line using your calculator and understand what it is used for (and how to use it).

I also handed back your tests from last week. Overall they were very good! Another job well done. Be sure to review ALL of your test material for the midterm this Friday!

We also looked at some Problem Solving situations using the material from the last chapter. You should have problems 1-7 (skip 2, 3, and 5) done for class tomorrow.

Have a great week!

Coming up:
- Homework: p. 125 #'s 1-7 (skip 2, 3, and 5)
- Midterm this FRIDAY!!!!!!

Posting for Points:
What is your favorite TV show? (We will use this data tomorrow)

Variation

We started the day by looking at the graphs for both our M&M data, as well as the Starbucks data. Make sure you know how to plot data on your calculator, find the regression line, and understand how to put that information back into the context of the problem. This material WILL be on the midterm.

We discussed 4 different types of Variation: Direct, Inverse, Exponential, and Joint. Be sure that you know the equations and standard shape of these relationships. If you still have questions, check out the links to the right.

Have a great weekend!

GO HEELS!!! Check out Late Night With Roy at Tarheelblue.com this weekend

Coming up:
- Homework: pg. 109 #'s 9, 11, 12, 39-44, 68
- Midterm next week!

Posting for Points:
Which school will have the best college basketball team this year????? (There is only one answer)

M&M Data

Today you guys split up into groups and took data on 10 fun size bags of M&M's. You should have taken data on several variables including: weight of bag, # of M&M's per bag, # of each color, etc.

In class you completed a set of questions dealing with the graph of the Weight vs. # in each bag, and found the regression line for this data. We will discuss this data tomorrow, and use the Starbucks data to create another plot.

Coming up:
- No Homework for tonight, unless you did not finish your Graph in class
- Midterm next week!

Posting for Points:
What does the correlation coefficient tell us about a graph?

Test (Transformations and Inverse Functions)

Today was your third test!! Hopefully everyone thought they did well! You will get them back as soon as everyone has taken the test.

Coming up:
- Tonight you should rework the problem that was one the board at the end of class
- Be sure you have your Starbucks data with you tomorrow (just the table)

Posting for Points:
What did you think of the test?

MATHO and Test

Today we played a review game preparing for the Test tomorrow. Review all of your notes (library of functions, rules for functions/transformations, etc.) and be sure that you work out a few more problems. Also, as discussed in class, be sure to remember your parentheses when needed (especially when working with composite functions). DISTRIBUTE THE NEGATIVE!!!

Good luck studying!

Coming up:
- Test tomorrow!!!
- Midterm next week! (We will talk about this on Thursday)

Posting for Points:
What do you think is the best way to study for a math test?

Mathematical Modeling

We spent the first part of class finishing up the review problems and answering any questions about the test material. Be sure that you correct and review all of these problems for your test Wednesday.

After the review problems we introduced Mathematical Modeling, the process of analyzing and interpreting data. We learned the process for graphing statistical data, as well as finding the Linear Regression line for any set of points. Remember, when looking at a linear regression line you use the correlation coefficient to determine how exact your line fits the given data. The closer to 1, the better the fit. If you need a review of how to graph this data on the calculator click the link to the right.

For this weekend you need to do some research on the exponential growth of the Starbucks franchise. You should use the link on the right and navigate through until you find the Company Timeline. Read over the timeline as it gives interesting information. As you go through the information create a table of growth since the first franchise. Your first year will be 1971 when the first Starbucks opened in Seattle. Start this year as 0, and continue up from there. Notice that there will not be a number for every year, so only include what is given in this timeline. We will use this data next week!

Have a nice LONG weekend!

Coming up:
- Homework: Create a table of values for the year and # of Starbucks stores at the end of that given year.
- Test will be Wednesday October 10th!

Posting for Points:
Where was the first Starbucks? Are you a Starbucks fan?

Test Review

Today we reviewed the material that will be on your test this coming Wednesday. Please remember that this test will be cumulative!

Tomorrow we will begin looking at new material that will not be expected for the test.

Coming up:
- Test on Wednesday October 10th
- "Midterm" coming up on October 17th

Posting for Points:
What does it mean if you find the fog and gof of two functions to both equal "x"?

Inverse Functions

Today we went over your assignment from page 99, dealing with inverse functions. We got through most of the assignment but you should all work on your given problem for homework.
We will go over these tomorrow (you will be the "experts") and then we will go over your review assignment.

I have decided that the test will be moved to WEDNESDAY, October 10th. Please begin studying now because we will move on to new material starting Monday!

Coming up:
- TEST: Wed. October 10th (remember that the test is cumulative)
- No Homework, but begin studying!

Posting for Points:
What is the BEST method for determining if one given equation is the inverse of another inverse equation?

Stuck in the Airport

I am stuck in the airport until late tonight but just wanted to remind you that you should have both Monday and Tuesday's assignments done by tomorrow. If you have not done them already, be sure to finish them tonight!

See you tomorrow!

Coming up:
- Both assignments due tomorrow (from Monday and Tuesday)

Posting for Points:
Who has the worst luck with flying?

Composite Functions

We started today reviewing Transformations, specifically #'s 13-18 on pg. 80. Be sure that you have a strong understanding of how functions move. Remember to check out the link on the right if you are still having trouble with transformations.

We took a few notes on Composite Functions (basically operations for putting two functions together). Be sure that you simplify all of your composite functions!

Coming up:
- Homework: pg. 89 #'s 6-12 even, 17, 18, 31, 33
- Your next test is October 5th!
- Remember to meet OUTSIDE tomorrow for class. Meet at the courtyard steps over by the gym!


Posting for Points:
When is your next test?

Translations

We went over translations during the entire class period today! Hopefully you are beginning to see how these functions move, but it can take some time before this material really clicks. Be sure to check out the websites on the right, especially "Visual Functions," if you are still having trouble with these problems. We will spend a few minutes tomorrow going over Transformations, but then we will be moving on to Composite Functions.

Composite functions are pretty easy because it is just performing basic operations on 2 functions instead of 1. For example, (f+g)(x) = f(x) + g(x)....so if f(x) = x + 3 and g(x) = 2x + 2 then, (f+g)(x) = (x +3) + (2x + 2).....or simplified.... (f+g)(x) = 3x + 5

We will go over this tomorrow but you should look through the examples on pages 84-85 before class. This is your only homework, other than the question below, but make sure you do it!

Have a great day!

Coming up:
- Homework: Read over pages 84-85 and review your homework from last night; Also complete pg. 80 13-18
- Your next test will be Friday, October 5th!

Posting for Points:
Using your book and/or the brief notes from above, what would (f - g)(x) equal ? (it follows the same pattern as above)

Transformations

A few key points from last night's homework:
a) be sure that you have corrected the Greatest Integer Function as always rounding DOWN!
b) review how to read function values as coordinates. After reviewing the homework we created a key for Transformations (the way our standard graphs move). You should keep these notes with your Library of Functions.
For tonight be sure that you check out the website under math links labeled "Visual Functions." This website should help you visualize how translations occur. (Section 1.7)

Have a great day!

Coming up:
- Homework: pg. 79 #'s 1, 2, 4, 5, 9-12
- You will get your tests back tomorrow!

Posting for Points Question:
How will this function move from our standard graph of f(x)=x:
f(x)= x + 3

Library of Functions

Today we created a library of 10 functions which you should keep in your notes. Be sure that you have all 10 because it will make transformations much easier if you know what the standard graph looks like. We also talked about reading function values as coordinates and creating the equation of the function using those values. (Section 1.6)

Have a great week!

Coming up:
- Homework: pg. 71 #s 2-24 even, 29, 31, 43, 44
- You will get your tests back Tues. or Wed.

Posting for Points Question:
What is the name of this function: f(x) = c

Second Test!

Today was your second test!! Everyone seemed to do well as I glanced through them. From now on you can come here to find out what we did in class, as well as what assignments you should be preparing for. I will also post notes and examples here occasionally so you should check this often.

Have a great weekend!

Coming up:
-We will begin looking at transformations of functions Monday (section 1.6)
-Your next test will be 2 weeks from today (Friday, October 5th)

Posting for Points Question:
From now on you will find a question here each day relating to new material learned in class. You will post a comment in response to the question and recieve 1 point for a correct answer. It will be required that you answer at least 3 each week!

For this weekend just submit a comment and say HI!

Welcome!

Welcome to the Math Analysis Blog.

The main purpose of this blog is to allow anyone that misses class to see what material we covered, as well as find some notes and diagrams used during that day's lesson.

There will also be questions posted each day. You MUST answer at least 3 questions each week as part of your weekly homework grade. You should check this website often for updates and notes!