notes p.2 – the cartesian coordinate system. i. cartesian plane the xy-axes named after reneé...
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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.