Optional Alg II Project [Due by 4 pm on Tuesday, May 21, 2013]
The objective of this project is to create an “artistic drawing” by combining at least 3 of the 4
conic section relations in a single graph. Linear equations may also be used. The final product
will consist of three components:

A graph finished as artistically as possible—with no visible algebraic symbols. You
may color/paint/shade this graph by hand. This drawing will be on paper.

A second graph (or graphs if a single graph is too cluttered) consisting of labeled
curves. This graph (or graphs) may be drawn electronically.

A table listing all of the relations, complete with labels, relation types, and
restrictions. This table may be created electronically.
Example
y
B1
C1
8
A1
6
4
C2
B2
2
D1
0
-2
A2
G
D2
A3
-4
F
This is the image that
was being attempted.
-6
E
-8
Restrictions
𝑦≥0
−6 ≤ 𝑥 ≤ −3.5 & 𝑦 ≤ 0
0
2
4
6
8
3.5 ≤ 𝑥 ≤ 6 & 𝑦 ≤ 0
(𝑥 − 6.25)2 + (𝑦 − 6.25)2 = 8
𝑦≥0
𝑦≤0
2
2
(𝑥 + 6.25) + (𝑦 − 6.25) = 8
𝑦≥0
𝑦≤0
2
2
𝑥
(𝑦 + 1.5)
8
D1
Ellipse
𝑦≥0
+
=1
3/2
9/16
9
D2
𝑦≤0
2
10
E
Parabola
−4 ≤ 𝑥 ≤ 4
𝑦 + 7 = 0.18𝑥
11
F
Parabola
𝑦 + 6.1 = 0.23𝑥 2
−5 ≤ 𝑥 ≤ 5
2
2
𝑥
(𝑦 + 1.2)
12
G
Ellipse
−4.2 ≤ 𝑥 ≤ 4.2 & 𝑦 ≤ 0
+
=1
19
9
The drawing may be a cartoon figure (other than Mickey Mouse, obviously) or something real
(such as a flower, car, landscape); however, abstract artwork will not be accepted. The drawing
must actually look like something that is easily recognized.
1
-82
3
4
5
6
7
Label
Type
A1
Circle
-6 A2 -4
-2
A3
B1
Circle
B2
C1
Circle
C2
Relation
𝑥 2 + 𝑦 2 = 36x
The types of relations you may use are listed below.
Possible Relation Types (In the Form Needed for the Table)
𝐴𝑥 + 𝐵𝑦 = 𝐶
Linear
y
6
Parabola
𝑦 − 𝑘 = 𝑎(𝑥 − ℎ)2
4
Circle
(𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2
2
(𝑥−ℎ)2
Ellipse
𝑎2
Hyperbola (1)
(2)
(𝑥−ℎ)2
𝑎2
−
+
−
2
(𝑥−ℎ)
𝑎2
(𝑦−𝑘)2
𝑏2
(𝑦−𝑘)2
𝑏2
h=4
k=1
a=2
b=3
-2
=1
Ellipse
2
4
x
6
8
-2
f(x)=sqrt(3^2*((1-(x-4)^2/2^2)))+1
-4
f(x)=-sqrt(3^2*((1-(x-4)^2/2^2)))+1
=1
2
+ (𝑦−𝑘)
=1
2
y
𝑏
Hyperbola (1)
6
h=4
Exponential
𝑦 − 𝑘 = 𝑎𝑏 (𝑥−ℎ)
4
Logarithmic
𝑦 − 𝑘 = 𝑎 ∙ 𝑙𝑜𝑔𝑏 (𝑥 − ℎ)
2
ℎ)
-2
k=1
a=2
b=3
2
4
x
6
8
-2
f(x)=sqrt(-3^2*((1-(x-4)^2/2^2)))+1
-4
f(x)=-sqrt(-3^2*((1-(x-4)^2/2^2)))+1
This Word document can be downloaded from the OCC. Once you have Graph 4.3 downloaded
and installed, you should be able to open the Mickey graph in this document (either by double
clicking or right clicking it) and start playing with the software and see how easy it is to use. (A
curve or label can be easily turned on or off by clicking the checkmark in the square left of the
equation or label.) When you are ready to type your table, I recommend you start with the table
in this document and edit it. (Rows can be inserted by right clicking. The equations and
restrictions can be edited using the Microsoft Equation Editor found on JP2’s laptops.)
Expect to do a lot of playing (trial and error) to create your figure. I did with Mickey. Have fun!
Rubric
Artistic Drawing (recognizable object, attractive, etc.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20%
Graph of equation (consistent with the artistic drawing) . . . . . . . . . . . . . .
20%
Table (equations and restrictions consistent with drawing . . . . . . . . . . . . . . .
30%
Following Directions (labels, minimum number of curves and types) . . . . . . . . . . . . . . . . . 30%