Chapter 2 Project - Chapter 2 Review # 84

Exploration 1:

Exploration 2:

Exploration 3:

4.8 Project

Chapter 1 Project

For this project on regression, I chose option 5 .

Ch. P - Graphing Functions

Black: y= |x| Parent

Red: Vertical translation y= |x| + 8

Blue: Horizontal translation y= |x-5|

Green: Vertical + Horizontal translation y= |x-7| - 2

Purple: Reflection over x-axis y= -|x|

Black: y= -|x+10| - 4 Vertical + Horizontal Translation + Reflection over x-axis

1. My starting(parent) equation was y=|x|

2. I performed a vertical translation on graph 1 which shifted the graph up by 8

3. I performed a horizontal translation on graph 1 which shifted the graph to the left by 5

4. I performed a vertical AND horizontal translation on graph 1 which shifted it to the right by 7 and down by 2

5. I performed a reflection over the x-axis on graph 1 which changed all the y values to opposite

6. I performed a vertical AND horizontal translation on graph 1 and also did a reflection over the x-axis which moved the graph down by 4, to the left by 10 and changed the y values to opposite.

Ch. P - Applying Linear Equation in Two variables

For this project, I chose to do problem #8 on page 38. The problem required:

(a) Write a linear equation for Americans' income in y in terms of the year x using the points (1998, 7.4) and (1999, 7.8).

First - I used m= y2 - y1/ x2-x1 and substituted my points in to find the slope.

Second - I used slope-intercept form which is y=mx + b to find the linear equation so I can get the y-intercept.

Third - I get my equation which is y=0.4x - 791.8

(b) Use the equation in (a) to estimate Americans' income in 2001.

First - Find y when x=2001 in slope-intercept form. Put 2001 in for the x value in the equation from (a).

Second - The answer will be 8.6 trillion which is only 0.1 off from 8.7 trillion.

(c) Use the equation in (a) to predict Americans' income in 2008.

First - Use the same steps as (b), but instead of 2001, use 2008.

Second - The answer will be 10.4 trillion.

(d) Superimpose a graph of the linear equation in (a) on a scatter plot of the data.

First - I used my graphing calculator to make my scatter plot by plugging in all the points.

Second - I pressed the [Y=] button and plugged in my equation from (a).

Third - You will see a line running through the first 2 points in your scatter plot and touching the other points.

By finding the slope and using the slope-intercept form to write a linear equation, I am able to estimate and predict Americans' income for any year that I want.

About Trinh

Education: Pham Ngoc Thach 1st-4th

La Esculita Elementary School 4th-5th

Westlake Middle School 6th-8th

Oakland High School 9th-10th

Work and Volunteer: buildOn club at Oakland High School

When I grow up: I want to pursue a career either the medical field or in biology for now.

I love: Playing games on the computer ( especially shooting games xD ), playing sports, reading mangas ( Japanese comics ), watching Discovery channel and chatting with my friends on my AIM/phone.