Graphs and Quadratic Functions

Today in our math class we reviewed how to sketch the graph of a funtion. When given a function the a part of the equation is the x squared part, the b part is the x part of it and the c is the y intercept. You can use the c to find your y intercept when graphing. you can also use a table of values to find where numbers repeat. Where they repeat will get you close to the max or min value. If the function opens up there will be a min value and if it opens down there will be a max value. The axis of symmetry is the line that goes through the point of the function, the max or min value. We then ended off the class by doing an assignment on pg. 368-372 questions 1,3,4,6,7,9,11 part i and ii and 13.

Next person to go will be Koralyn

Project Hand-in

Please, have your files prepared for your presentation. You should either bring your files on a memory stick or email them to me at mrbanow at gmail.com. 


Please, do not plan to sign in to your email account or school account.

Project Info Re-Posted

Here is the Project Assignment if you have misplaced it: http://dl.dropbox.com/u/39411274/Math%20Foundations%2020%20Project.docx

I have decided that giving you the Holiday Break to finish your projects may be better than having them due before the break. Presentations will be on Wednesday, January 4 and Thursday, January 5. If you would prefer to present before the break, speak to me and we will arrange that.

The presentations will be as follows:

Wednesday, January 4
Michelle
Aaron
Alex
Kelsey
Jeff
Nina
Brydon
Emily
Colby
Joel

Thursday, January 5
Sarah
Amy
Koralyn
Allysa
Tanner
Cody
Taryn
Miranda

You should email your presentation and other files to be displayed on the SmartBoard ahead of time. Email my mrbanow at gmail.com account. If you have any materials that are not digital, please bring them the day of your presentation and hand them in to me.

If you have questions now or over the break, email me and I will get back to you fairly quickly.

Good luck and have some fun! I hope your topic interests you!

Next Stages in the Project: Data and Controversy

In chapter 5, we studied measures of central tendency and Normal Distributions. Depending on your topic, this may relate to your project. If you have done a survey or have collected data (even from online), then you will want to consider how to analyze your data:

• will you discuss mean, median, or mode?
• is your data Normally distributed?
• do you know that sample size and margin of error/confidence level for the data you found online?
• see pages 284-286 for more suggestions

Now that you have completed some research, you will want to scrutinize your data for any controversial issues. 

• have you found two sources that provide contradictory information or data?
• does the contradictory data represent different viewpoints? (eg. is the data being provided by a group that would want a certain outcome?)
• see pages 352-353 for more ideas

Everyone needs to follow this link and complete the short survey regarding your controversial issue(s). 

CLICK HERE ----> Complete this once you have done a significant amount of research

If applicable, discuss the controversial data in your presentation.

Chapter 6 Review Answer Key

Click here: http://dl.dropbox.com/u/39411274/Review%20Answers%20Ch%206.pdf

6.6 Optimazation Problems: Linear Programming

On Tuesday we started 6.6 Linear Programming. Linear Programming is a mathematical technique used to determine which solutions in the feasible region result in the optimal solutions of the objective function.

To solve this, first you find the linear inequalities and put them on a graph. After that you fine the maximum and minimum values of the objective function. You can do this by using a vertex/value chart. Then using the information from this chart make a statement showing your results.

We were given five steps in using Linear Programming to solve an optimization problem which includes the information we have learnt in 6.4 , 6.5, and 6.6.

The steps are as followed:

1. Define: - Variable

- Domain/Range

- Inequalities (Constraints)

- Objective Function

2. Graph

3. Evaluate the objective function at the vertices's

4. Analyse and Interpret - choose desired solution

5. Verify

After we went through EX.1 on the handout Mr.Banow gave us. Question found below in picture.

For practise we got assigned Page 341-345 # 1,2,4,6,11,13

:)

6.4 and 6. 5 Optimization Problems

:)

In 6.3, we learned that what kind of numbers were dealing with contribute to our answer. This still applies to 6.4.



In 6.4, we learned about optimization problems. In an optimization problem, it asks you for the maximum and minimum possible solution.

Optimization problem
a problem where a quantity must be maximized or minimized following a set of guidlines or conditions.

Constraint
A limiting condition of the optimization problem being modelled, represented by a linear inequality.



Objective function
in an optimization problem, the equation that represents the relationship between the two variables in the system of linear inequalities and the quantity to be optimized.

Feasible region
The solution for a system of linear inequalities that is modelling an optimization problem.

The area in yellow represents the feasible region.



When graphins linear inequalities we must remember which part of the inequality goes on certain areas of the graph.



We then went over the last page of our 6.4 booklet.
We found out that you can tell you're dealing with an optimization problem if you have to find the minimum or maximum.
We found that the constraints are the linear inequalities in the problem.

We did practice on pages 330-331 # 2,3,5,6.

In 6.5 we looked at the race car and suv problem again.
We realised that the maximum and minimum was on the vertices of the feasible region, but we had to find out which two vertices.

The objective function to optiimize was: C = 8r + 12s
C = cost
r = race cars
s = suvs

We found that (60, 40) was the maximum.
C = 12(60) + 8(40)
C= $1040

We found that (30, 40) was the minimum.
C = 12(30) + 8(40)
C = $680

But does the minimum cost satisfy all the constraints?
Constraints:
r<40 (less than or equal to)
s<60 (less than or equal to)
s+r>70 (greater than or equal to)
YES IT SATISFIES ALL CONSTRAINTS!

We then did practice questions on pages 334-335 #1-3

here is a math video to brighten your day! lolol
http://www.youtube.com/watch?v=cgEuUzHYvOY">


Next will be Aaron :D