2nd block: 10/28/08 October 29, 2008

on tuesday we learned about the long but helpful Rational Function

a long method to find the two equations
that are been divided and not using the calculater
and we took a quiz

the way i solve this a problem like this was
to first find the multiplying binomials, then find the domain, after you find
that you go to the hole and see if their is any binomials crossed out if so
youll make it equal to zero and solve it,

after that you go to the horizontal and vertical asymptote by dividing and solving to zero, but you’re not done
then youll have to find the y and x intercepts on dividing and solving
for zero, very complicating to remember but nothing impossible.

by:jonathan cordova

2nd block: 10/28/2008 October 29, 2008

Today in class we had a quiz on solving Rational functions, we had to figure out many different things such as the Y- intercept, the X- intercept, the hole, domain, Vertical Asymptote, and Horizontal asymptote. We  also had to label those on a graph that was given on the quiz. I personally think that the hardest part on the quiz was that I got the Horizontal and vertical asymptote mixed up, but I’m pretty sure i figured it out. =]After the quiz we got our last test back, and had 30 mins to correct any answer that was wrong. After you get the answer you had explain in a sentence or two, what you did wrong on the test, You were allowed to use your notes, text book, and/or ask Mrs. Hawn for help =] .

Christina Chamra

1st block: 10-22-08 October 25, 2008

In class today we reviewed using difference of two squares,trinomials,and also using four numbers when factoring in other words grouping. here  are some examples of what we reviewed:

Step1: write down the problem.

2x^2 +3x -14

Step2: is to see if the problem has a GCF.This problem doesn’t have a GCF.

Step3:Next is tom set up the diamond but sense I can’t write the diamond out I’ll just put out the factors.

( x +7)( x -4)

Step4:Now you have to divide by the A term which is 2.

( x +7)( x -4)

2       2

( 2x +7)( x -2)

We learned something even newer. were going over something new called rational functions.

Here is an example of a rational function:

f (x) =   1 + 2

( x -4)

This is called a transformed function.

Now you have characteristics of the function.

Transformations: right 4,up 2

Domain: 0

Vertical asymptote:x = 4

Horizontal asymptote:x = 2

x- intercepts:(3.5,0) <- [2nd][trace] 2: zero

y- intercepts:(0,1.75) <- [2nd][trace] x = 0

-Cynthia

1st block: 10/24/08 October 25, 2008

Today in class, we had a subsitute and he gave us a worksheet on Rational Functions that was similar to our notes/homework from yesterday. Our subsitute went over problems 1 and 4, then had us work on 2 and 3 on our own. After that, we played a game with the whiteboards. Everybody was in 3 groups of 7 and he gave us problems on the overhead and we worked together to find the x and y intercepts, horizontal asymptote, vertical asymptote, domain and hole. The first group to get them all got a point and the group with the most points won and got candy at the end of class.

Amber Battle

Today in Class 10/23/08 October 25, 2008

Today in class we had a sub because Mrs. Hawn was absent. We completed a warm up and finished the worksheet that was given to us yesterday on 10/22 on factoring functions. Then, the sub went over a flow chart for our notes on rationalizing functions. We discussed how to find the domain, hole, vertical asymptote, horizontal asymptote, y-intercept, & the x-intercept in that exact order. After a few examples on the board, we had the rest of class to work on problems 1 & 2 on the other side of the flowchart worksheet. Tomorrow, we will continue to work on rationalizing functions to get a better understanding of it. Mrs. Hawn will be back on monday

-Lyndsay Bradford

Block 2

1st period: 10-21-08 October 22, 2008

October 21st we took the Unit 4 Test.  The test consited of questions about graphing and solving cubic functions through synthetic division.  Cubic regression, volume, and a review of area.  Each question of the test had a point value and you could omit up to 10 points.  Depending on the point value this could be 1 question or several.  This system was a great way to  not be penalized if you were unsure of a question.  I thought the hardest part of the test was the area questions but the synthetic divsion was really easy.

-Kristina

1st block- 10-17-08 October 20, 2008

We are learning about cubic functions, which are similar to quadratic functions except for a few details. The standard form of cubic functions is ax^3+bx+cx+d, they all have 3 roots, and the domain and range of cubic functions is all real numbers. We are also learning about modeling with cubic functions, which can be used to find the greatest volume made from a sheet of paper. We have also learned about synthetic division, which is a shortcut method of polynomial division. I find this the easiest because it doesn’t involve the calculator and it is a throwback to long division, which is something I remember completley. I still have trouble finding the real root of problems like y^3+27= 0, then using synthetic division to factor. Cubic regression is hardest for me, because I confuse it with quadratic regression.

1st period: 9.23.08 October 19, 2008

today we learned how to solve quadratic equations.here are some examples on solving these equations.

Step1: first you set the equation equal to zero.

x^2 – 4x -12 = 0

Step2: you set up the diamond and scents I can’t write that out on the computer I’ll just write out the way to solve for the roots.

(x-6)(x+2)= 0

Step3: then you solve for the x-intercepts,zeros,solutions,etc.you would have to add six on both sides and also subtract two on both sides.

x-  6 =  0         x+2  = 0

+6    +6            -2  -2

x= 6                 x= -2

we also analyzed Graphs of Quadratic functions.here are how they are solved step by step including using how the graph will be shaped like if it opens up or down and the graph is shaped in a U like shape. it can also get skinner or wider if the equation has a lower number used in it will most likely get wider in size.if the a variable is negative the parabola will open down which is also called a maximum. and if the number is positive the graph will open up which is also called the minimum.

Step1: y=a(x-h)^2-k

h=1

k=3

-15=1(-2-1)^2-3

this means that it will open up which means it will have a minimum. it moves right one and shifts down three.these problems are very fairly easy to me but at first it takes some hard work to get it.

-Cynthia

3rd block: 10/14/08 October 15, 2008

Today we learned how to solve cubic equations. First, you find the root that goes in the box and then you draw a line and at the top of the line you put the numbers that you figure out form the equation and then you multiply the root by each number and put the answer at the bottom of your top number and one space to the right and add the botton number and the top number.then, you find the answer by making another equation with the numbers that you got when you added the numbers but with one exponent down.l

Block one: 10-06-08 October 15, 2008

Today in class we reviewed Quadratic equations for the test on 10-07-08. Some of the examples givein were.

 x^2+8x+7

• The vertex would be (-4,-9)
• y less than or equal to -9= This is the range
• (0,7)= y-int
• Domain: all real number’s

Another way is to solve inequality algebraically (find zeros once in std. form)

Ex: x^2-4x+3<0

• Greater then and less then= open circle on the number line.
• Greater than and equal to and less then and equal to= closed circle on the number line.

steps:

1. Put in standard form find zeros (x^2-4x+3=0)
2. Then you would put this equation in a diamond. (x-1)(x-3)=0, x=1,3
3. Then draw a number line, put open or close circles on zeros.
4. Test=o (0^2-4 x 0+3>0)= 3>0 this is correct because three is larger then zero.
5. Write solution in set notation x<1 or x>3.
6. Then graph equation.

Graphing inequality: y greater then or less then ax^2+bx+c

Ex:2 y>x^2-3x+2

1. Graph equation with solid/ dashed line.
2. Test (0,0)= 0>0^2-3 x 0+2= 0>2 this is not true.
3. Shade in area that makes inequality true.

• Dashed is when it is greater then or less then.
• Dotted is when it is greater then or equal to or less then or equal to.

2nd Block: 10/13/08 October 15, 2008

Today we started off the period with a warm-up.  1/2x³-2x²-2x+8, we had to find the roots, which were {-2,2,4}. Then we took guided notes on Synthetic Division. It wasn’t to difficult but the steps are

1. Find the root that goes with th binomial factor

2. Is to make the chart that the teacher showed us

3. Solve

4. The result is now the coefficients of an expression with one less degree

Then we took more notes on Synthetic Division with a possible remainder. Which is basically the same as the first thing but it isn’t always equal to 0. It was all pretty easy and the block went by really fast.

3rd period: 9/19/08 October 13, 2008

We’ve started on a new problem (discriminant). It is D=b^2-4ac. We solve this first by graphing the proplem first. And the problem should come out as a parabola. The problem might be a perfect square a not perfect square, zero, or a neagtive. A perfect sqaure has 2 rational roots, a positive, not perfect square has 2 irrational roots, zero has 1 rational root and a negative has 2 complex roots.

2nd period: 10/13/08 October 13, 2008

Today we did synthetic division. with synthetic division first you need to find the root that goes with the binomial factor. then you examine the work below and find where the pieces came from.the next step is to solve in order to solve you need to follow the steps as listed:1) bring the first coefficient down 2) Multiply it by the number in the box 3) Write it under the next coefficient 4) Add the two numbers together and lastly you repeat until the last coefficient. The final sum will be zero.When you get to the end of the problem and you want to show what your answer is then the result is now the coefficients of an expression with one less degree. Then you would write the variables back starting with x2 and decreasing in order.

i understood what we were doing in class very well and if i got stuck on a problem i looked at the problem to see if i wrote something wrong and then i referred to my notes and if i still didn’t understand what i was doing i asked ms.hawn for help and she helped me out with the problem that i was stuck on.

-Caprice

1st period: 10/9/08 October 13, 2008

Today in class we learned about cubic functions.  After puting the equation in standard form you find the different peices such as: Y-int, local min, local max, # of real roots, and real roots.  we also compared and contrasted cubic functions and quadratic equations.  we found that the range of cubic functions are all real numbers.

-Michele

2 period- 10/9/08 October 13, 2008

today in class we did a poster on comparimg quadratic funcctions to cube fuctions. and then we did graphing cubic forlimas. then we went over our homework. we learend a new standard form to do transformations.