Some extra help on Quadratic Functions

Here is a video that shows the basics of a Quadratic Function.  It reviews the vertex, axis of symmetry, zeros and how to calculate them. 




This video goes through and explains how the values of a (or c in the video)change the original graph of y = x^2. 


This next video reviews how q effects the graph.



This last one is on p.

Blog Prompt: I'm seeing Purple.....

I'm seeing Purple... Purplemath that is. 

We're learning about quadratic functions. You can find an excellent four page tutorial here. It is a little more indepth and gives more details then your worktext.  The site is called Purplemath. It's really well done. It may even be worth spending some time there exploring.

BLOGGING PROMPT

Explore Purplemath website.   Pick a topic that you have had difficulty with and see if you can find a tutorial that you find useful in explaining the concept.  Post the link to the page and blog on how it helped the 'light turn on' for you. 

 

Analyzing Quadratic Functions in Standard Form

Over the weekend you need to finish Checkpoint 1 on page 272 - 275 if you did not finish it in class on Friday.   You also need to complete the Construct Understanding on page 276 and read the summary of Lesson 4.3 on pages 277- 278.  Check out this website to see how the values of  a,  p (h in the applet) and q (k in the applet) effect the graph.  You may also find it beneficial to read through the examples as we will be going through them in class on Monday. 

Standard Form of a Quadratic Functions
The Standard Form of a quadratic function is: y = a(x – h)^2 + k or y = a(x – p)^2 + q
If a quadratic function is written in this form, then it will have the same shape as y = ax^2 and its vertex will be shifted from (0,0) to a new location as determined by the values of  p (or h) and  q (or k) .
TIP: The value of “a” gives you the shape of the graph and the values of “p” and
“q” tell you the location of the vertex.

Blogging Prompt: Quadratic Functions

Use your graphing calculator (or an online tool; x² is written as x^2 and do not include the "y=".) to graph these three functions (y is the height and x represents time):

• The height of an arrow is given by: y = -16x² + 112x + 0
• The height of a baseball is given by: y = -16x² + 64x + 0
• The height of a football is given by: y = -16x² + 64x + 75

Blog a brief paragraph identifying ways in which these three functions are similar. Blog a second paragraph outlining the ways in which they are different and what causes these differences.

This sort of compare and contrast exercise can be made easier to do using Venn Diagrams. Draw three large overlapping circles. List the similarities in the appropriate overlapping sections and the differences in the non-overlapping sections. If you like, you can use this web tool to do it online. If you do blog about this prompt and want to post your diagram and don't know how to post pictures, ask in class. ;-)
Note:  This blogging prompt was copied from Darren Kuroptawa's Pre-Calculus 30S blog.

21st Century Education

21st century education is a new way of teaching which will use some of the resources that have improved drastically since they started schooling the 19th century, including technology communication, and interactions with other students, and teachers. The way they began teaching school in the 19th century was to try and prepare children for life in the industrial economy. This new way of learning will help students to learn skills that will be needed to succesfully help serve the needs of people in this century. This program is experimental, but it is giving students a better chance of succeding in whatever field they plan to be in once they graduate.
Some skills needed are:
*Adaptability/Managing Complexity and Self-Direction
*Higher Order Thinking and Sound Reasoning
*Interactive Communication
*Effective Use of Real-World Tools
*Personal and Social Responsibility
*Teaming and Collaboration

I believe that the most important skill in 21st century education is "Interactive Education". My reasoning for this is there are very few things that can be done in this world if people do not communicate. With the technology that can be used in the present day we are able to communicate with people from all over the world. Even if we are not communicating with people from all around the world it is essential that we are able to communicate with people in small groups and workplaces. I think that 21st century education is a great way for students to start learning, it'll give them a great grasp on the skills they need in both the old and new economy.

Pre Test Blogging

Well, there are things that I found hard with this unit, like completing the squares, and some of the factoring. But other things like defining how many roots or answers a question has and some of the easier factoring was not too bad. Im worried about the test, but with doiumg some studying on the weekend I should be fine with it, and hopefully do okay in the end!

blog before a test.

i found the skillls summary page to be very helpful outlining what we learned in class on one page. i always love having pages like that because it outlines what is on the test , so i go through it to see what i know and dont know. i think it will help me study this weekend. i am nervous because the test is on a monday and on mondays i feel like a blank slate. also binomials are the trickest thing to me. wish me luck!

unit 3 test

I found that this unit had parts that were fairly difficult, and parts that were fairly easy. The factoring trinomials and binomials were fairly easy. The part I found difficult was solving equations using the completing the square method. I enjoyed figuring out how many roots equations had. Overall this unit was fairly good.

Pre-test Blogging

This unit had its difficulties but I found that I eventually got the hang of it. Factoring polynomials and trinomials wasn't too hard because it was an add on to last year's work. I enjoyed finding whether an equation had none, one or two roots as I don't mind dealing with inequalities (that is, so far!), but found that some of the factoring- with decimals, fractions, etc.- to be a little tedious. All in all though, the unit was pretty good.

Completing the Square

This site reveiws how to factor a trinomial by using algebra tiles.

Look at this site and build some perfect squares. 

We will be using this concept to look at how to solve quadratic equations by completing the square.

Now it is time to practice.  Click here to go to an applet with practice questions.

Blogging Prompt: In Tune with Math

Wow, check this out. This guy records an original song a day. Not surprising that there is one that has math in it. But only one - a little disappointing ;(



This blogging prompt, should you choose to do it involves creating a song about math.   It can either be a song that talks about math in general or perferrably a song that decribes/teaches a math concpt that we have covered in class.  See the post on "Factoring to a beat!" for an example. 

This blog prompt can be done individually or in a group, as a class or even someone in Pre-Calc 40S.  Your song needs to be at least 1.5 minutes long.  You will need to record the song so it can be but on the blog.  A song by itself will be equivalent to 3 blog posts.  If you include a video then it will be worth 5 blog posts.  If you have any questions, be sure to ask. 

Have fun!!!!

This one is due by December 20, 2011

Solving Quadratic Equations

Here is a quick overview of solving quadratic equations.

Factoring to a beat

Here is a song to help you learn about factoring!

unit 2 pre-test response

In unit 2 we learned radicals and varients. It was just as difficult as the brief learning we did on it in grade 10 pre-calc. Although I havn't use these outside of school it still isn't that grogy of a subject. The only thing is i need to remember to use foil on questions like 4|53y|squareroot 70|8.

Test 2 pre-blog

Learning this unit I found not to be too difficult as it was a bit of a review from last year's simplifying binomials/trinomials. However it did have its new challenges having the radicals involved, but after several examples and explanations from Mrs. Frey I finally got the hang of it. The hardest part of this unit was remembering all the different ways of simplifying radicals and knowing how to apply them. Hopefully I know them now!

Education of the 21st Century

21st century education is the new education of our generation involving endless ideas and opportunities regarding our enhanced technology, communication and social interactions. It is so much more experimental and fun than passed education and is opening many more doors to students all around the world. Research is increasing and going more into depth and social acceptances are giving our generation and generations to come unending chances.

Skills needed include:

* Critical Thinking and Problem Solving

* Collaboration across Networks and Leading by Influence

* Agility and Adaptability

* Initiative and Entrepreneurialism

* Effective Oral and Written Communication

* Accessing and Analysing Information

* Curiosity and Imagination

I think that the most important skill for me is the “effective oral and written communication”. As technology is advancing we are able to connect with people all around the world for trade, business, or just acquainting. Without proper communication skills we would not be able to achieve very much. As most of what we are learning is coming through research that scientists and the like from all around the world are working together on, communications need to be there. Even within closer areas of work, communications is essential as we use communication to express ourselves and problem solve. Without communication we are not able to develop other skills needed for our 21st century lifestyles.

These skills can be incorporated into our classrooms through any means. When a problem arises we can take the time to try analyze what to do, find ways to fix it, use communications to ask questions, search out the answer by means of a computer network, and thus eventually figure it out. We could potentially use all of these skills without even knowing it. By practicing these skills and taking the time to think about how we can better ourselves with them, we as students are preparing for our future and the future of our world.

Unit #2 before test

The things that I found easy about this unit is, putting mixed radicals into entire radicals, and vice versa. The thing that I found more difficult that I now understand is rationalizing denominators. It didn't make much sense off the start but once I found out that you are just multiplying both sides by the conjgute, and then you are just simplifying it seemed alot easier. I haven't seen when you would use the things from this unit outside of school but I could see how you could use this outside of school.

Blogging Before a Test

Well this is where i talk about this unit went, right?
So here goes.
The main things i got out of this unit were things like how to factor, solve, simplify and rationalize equations and expressions that have radicals, and how to use absolute value to determine what value a variable could possibly be.
Most of the things in the unit went pretty well for me, which i am thankful for, but i did have some trouble with rationalizing, and solving some of the larger equations, but i managed to get it into a point of understanding in the end.
Well that is my thoughts on unit 2!

21st Century Education and Skills

What is 21st Century Education?
Well ,from my opinion, it is the way the new and constantly developing world around us has adapted to our society, changing it to fit the world we live in. This however, breaks out of the mold of education that we saw for so long. It is the new way that we set up the problems and the equally new way that we use logic and formulas to work our way through them.

What skills do i think are most important in 21st Century learning?
There are many different skills that 21st century learning has shown us, and they are all important skills to learn, or at least be familiar with. iI could not just choose one of these to be the most important so I chose 2.
First is Critical Thinking and Problem Solving. This is very important because it gets you to think about things in a different way, and stop and figure out the best solution for the problem, whether it be in the classroom or real life.
The second one that i chose was Agility and Adaptability. you need to be able to work efficiently and and quickly, but still get it done right. being agile helps with this and is very important. Adaptability is also important, because if you cannot adapt to the ever-changing world, you will quickly fall behind.

What do i think can be done to get these skills more in our classrooms?
well i really like that you took so me of the media things we are used to like computers, and incorporated math into it. it shows that they have already thought of a way to adapt into a technology based society and makes it new and more interesting to the students. Using different methods tho get through until, and different ways of teaching also keep it fresh.
one thing i think that they could do is make it a bit more interactive, but i am not exactly sure how. Otherwise, i like how this is set up differently from other courses, and i think they should keep working on that!

21st CENTURY EDU

im gunna have to go with 21st century education is just basically they re tryna evovle education. i assume they are tryna wein us off of teachers and practice more of a self learning style using technology.

faced with the fact that maybe the world is kinda screwed due to the fact of global warming, and other issues around the world such as famine and poverty and stuff , we need to arm students with the knowledge of being able to communicate effectively function and create change on many levels.

so some 21st century skills

1. critical thinking and problem solving

2.agility and adaptibility

3.effective oral and written(or typed) communication

4.being able to properly access and analize info and draw conclusions

5.intiative and entrepreneurilsm

6.collabouration across networks

7. having curiosty and imagination (if you dont have these go home)

the most important skills would have to be effective communication and being able to drawn conclusions from things

some new definitons

teacher-