Power Center Academy High
Pre-Calculus-McCloskey
CONICS SECTIONS PROJECT
Here is your task for the conic sections unit:
Make a picture which incorporates conic sections
That’s it. No catch. No tricks. Your job is to use the Desmos online calculator as a tool to graph
equations, forming them into a picture of your choosing. This is your chance to combine your keen
mathematical skills with your creative side. You may create your own unique picture or model after a
(school appropriate) picture of your choosing. Abstract art will not be accepted. This project has very
few restrictions, but here are the guidelines you need to follow.
Use the Desmos online calculator to create your picture. You will need to create an account with
Desmo. If you use Gmail, you can link your accounts so you will have a single log on for both. This
will allow you to save your work as you go along, then share your final product as a link. You will
want to consider restricting domains and/or ranges of your equations. (Restricting domains is part of
the grading criteria.) This will require some guess and check on your end.
Your final drawing must incorporate the 4 conic sections in a meaningful way. You may also
consider using lines and graphs of other functions you have learned (or not learned yet!). A minimum
of 3 parabolas, 3 circles, 3 ellipses and 2 hyperbolas are required in your picture.
When your picture is complete on Desmos, use “Print Screen” to move it to a drawing program, like Paint. Here you
can color it and edit out unwanted elements. (Remember that domain restrictions should be used.
You should have minimal unwanted elements to edit out.)You may color your drawing in Paint, or
print a black/white outline and color it in. Final submitted project should be in color.
How you will be graded.
Through this project, you are expected to demonstrate an understanding of systems of equations
involving conics by utilizing a variety of equations, and how they work together. This will be worth a
total of 40 points. The attached rubric breaks down point values into 2 categories:
The product: you will submit 3 sheets of paper: the Desmos graph with equations, the
completed picture, and the reflection essay as discussed below. Attach these to one sheet of
construction paper for submission. Please also email me the link to your graph:
amccloskey@powercenteracademy.org
(1) Graph, equations/restrictions, and final picture account for 20 points of final score.
(2) Reflection: write 500 words (750 words maximum) which explains the use of 3 equations (3
unique conic parent functions) from your picture. Discuss how you developed the equation, and
describe its role within your overall picture. This accounts for 20 points in final score.
Project Submission Date is Friday, October 3rd. *You will receive 1 bonus point for each day you
submit your project ahead of time starting Monday, September 29. For example, submitted on
Thursday, Oct 2 equals 1 bonus point. If submitted Monday, Sept 29, that equals 4 bonus points,
which equals an additional 10%!
CONIC SECTION PROJECT RUBRIC
Name:
Part 1
–
The Product
Final submission features all 4 conic sections prominently (minimum parent function
requirements are met and equations provided are consistent with graph.)
5
4
3
2
1
0
Use of domain restrictions to create a clean picture. (domain restrictions included
in final submission.)
5
4
3
2
1
0
Sophistication of use of conics in your picture
5
4
3
2
1
0
Overall effect, style, and color of picture.
5
4
3
2
1
0
Part 2
–
Reflection Paper
Clearly identifies at minimum 3 conics necessary to the picture
6
5
4
3
2
1
0
Student discusses the conic sections using appropriate vocabulary
7
6
5
4
3
2
1
0
Student discusses the role of the conic in the picture, including domain/range
restrictions
7
6
5
4
3
2
1
0
Total Score
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
1
2
3
4
5
6
7
Label
A1
A2
-8
A3 -6
B1
B2
C1
C2
8
D1
9
10
11
D2
E
F
12
G
Type
Circle
Relation
𝑥 + 𝑦 2 = 36
Restrictions
𝑦≥0
x
−6 ≤ 𝑥 ≤ −3.5 & 𝑦 ≤ 0
-4
-2
0
2
4
6
8
3.5 ≤ 𝑥 ≤ 6 & 𝑦 ≤ 0
2
2
Circle
(𝑥 − 6.25) + (𝑦 − 6.25) = 8
𝑦≥0
𝑦≤0
Circle
(𝑥 + 6.25)2 + (𝑦 − 6.25)2 = 8
𝑦≥0
𝑦≤0
𝑥 2 (𝑦 + 1.5)2
Ellipse
𝑦≥0
+
=1
3/2
9/16
𝑦≤0
2
Parabola
−4 ≤ 𝑥 ≤ 4
𝑦 + 7 = 0.18𝑥
Parabola
−5 ≤ 𝑥 ≤ 5
𝑦 + 6.1 = 0.23𝑥 2
2
2
𝑥
(𝑦 + 1.2)
Ellipse
−4.2 ≤ 𝑥 ≤ 4.2 & 𝑦 ≤ 0
+
=1
19
9
2
*Note this picture does not meet the parent function requirements. 2 Hyperbolas, 1 Parabola, and
1 Ellipse are required to meet the directive.
y
Required Relation Functions
Parabola
𝑦 − 𝑘 = 𝑎(𝑥 − ℎ)2
6
h=4
Ellipse
𝑎2
Hyperbola (1)
(𝑥−ℎ)2
𝑎2
(𝑦−𝑘)2
(2)
𝑏2
+
−
−
(𝑦−𝑘)2
𝑏2
(𝑦−𝑘)2
𝑏2
(𝑥−ℎ)2
𝑎2
=1
=1
=1
Hyperbola (1)
6
h=4
k=1
4
a=2
b=3
2
(𝑥−ℎ)2
y
k=1
4
(𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2
Circle
Ellipse
-2
2
4
a=2
b=3
2
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
-2
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
Possible Relational Functions
Linear
𝐴𝑥 + 𝐵𝑦 = 𝐶
Exponential 𝑦 − 𝑘 = 𝑎𝑏 (𝑥−ℎ)
Logarithmic 𝑦 − 𝑘 = 𝑎 ∙ 𝑙𝑜𝑔𝑏 (𝑥 − ℎ)
Trigonometric 𝑦 = 𝑎 𝑠𝑖𝑛(𝑏𝑥 – 𝑐) + 𝑑
Additional examples: