Notes P.2 – The Cartesian Coordinate System. I. Cartesian Plane The xy-axes Named after Reneé...

Notes P.2 – The Cartesian Coordinate System

I. Cartesian PlaneThe xy-axes

Named after Reneé DesCartes

Used to plot data points and determine relationships between data.

x

y

II. Scatter PlotsA. By Hand - Self explanatory!

B. By TI-83+/84

1.) STAT – EDIT – SET UP EDIT.-ENTER

2.) STAT – EDIT – enter data in L1 and L2.

Year Population

1995 21,000

1996 21,500

1997 22,700

1998 22,600

1999 24,000

2000 25,700

2001 27,200

2002 27,300

2003 28,000

Enter the data on your calculator and then follow along with my overhead!

III. Absolute ValueA. Magnitude or distance from zero

B. Properties

, 0

, 0

a aa

a a

0a

ab a b

a a

, 0aab

b b

C. Rewriting Absolute Value Equations:

Ex. 1 - ( ) 3f x x

3, 3( )

3, 3

x xf x

x x

Ex. 2 - ( ) 3 2 1f x x x

, 3

1( ) , - 3

21

,2

x

f x x

x

First, find where each separate part would equal zero

10 when 3,

2f x

Next, set up your intervals using only one ≤ and only one ≥.

, 3

1( ) , - 3

21

3 2 ,2

x

f x x

x x

Now, drop the absolute value signs and simplify the expression. This goes with the right-most part of the domain

Negate the entire expression. This goes with the left-most part of the domain

3 - 2 , 3

1( ) , - 3

21

3 2 ,2

x x

f x x

x x

Finally, subtract the second absolute value expression from the first, giving you the expression for the middle part of the domain.

We need to be able to do this for CALCULUS!!

3 - 2 , 3

1( ) 4, -3

21

3 2 ,2

x x

f x x x

x x

V. Distance Formulas:A. Number Line:

B. Coordinate Plane:

a b

2 2

1 2 1 2x x y y

VI. Midpoint Formulas:A. Number Line:

B. Coordinate Plane:

2

a b

1 2 1 2,2 2

x x y y

B. Standard Form Equation:

VII. Circles

2 2 2x h y k r

A. Def - All points in a plane equidistant from a particular point (h, k).

VIII. Quick ReviewComplete the in-class worksheet.