Honors College Algebra
Graphing Project
The purpose of this project is for you to program a graphing calculator to draw a picture that incorporates the
graphs of the functions and relations we have studied in College Algebra. You will need to use your knowledge
of transformations (horizontal shifts, vertical shifts, “stretches” and “shrinks”).
Here is the list of the functions that you can:
*Constant function
*Linear function
*Quadratic function
*Cubic function
*Absolute Value function
*Greatest Integer function
*Radical function
*Rational function
*Circles
*Ellipses
*Hyperbolas
Requirements (80 points possible):
1. Have a drawing of you picture on graph paper (5 pts.)
2. Originality/Creativity (5 pts.)
3. You must have an equation for each piece of the graph, classified of what they are (10 pts.)
4. Work showing the steps of solving for y (10 pts.)
5. You must use some sort of transformation on at least 2 of your equations (5pts.)
6. You must use restricted domains on at least 2 of your equations (5pts.)
7. You must have a minimum of 8 equations in your picture (5pts.)
8. Your picture must be recognizable (5pts.)
9. 3 different types of graphs (5 pts.)
10. 4th and 5th different graphs (5pts.)
11. 6th and 7th different graphs (5pts.)
12. Precision and accuracy (5 pts.)
13. A paragraph explaining what your picture is (5pts.)
14. A paragraph discussing any the following: (5pts.)
a. What you liked/disliked about this project
b. What you learned while doing this project
c. Problems that you encountered while doing this project
d. Suggestions to improve this project
15. Bonus points may be given for extra creativity.
Requirements (80 points possible):
___________Have a drawing of you picture on graph paper (5 pts.)
___________Originality/Creativity (5 pts.)
___________You must have an equation for each piece of the graph, classified of what they are (10 pts.)
___________Work showing the steps of solving for y (10 pts.)
___________You must use some sort of transformation on at least 2 of your equations (5pts.)
___________You must use restricted domains on at least 2 of your equations (5pts.)
___________You must have a minimum of 8 equations in your picture (5pts.)
___________Your picture must be recognizable (5pts.)
___________3 different types of graphs (5 pts.)
___________4th and 5th different graphs (5pts.)
___________6th and 7th different graphs (5pts.)
___________Precision and accuracy (5 pts.)
___________A paragraph explaining what your picture is (5pts.)
___________A paragraph discussing any the following: (5pts.)
___________Bonus points may be given for extra creativity.
_______Total (80)
_______%
Equation 1: _____________
Equation 2: _____________
Equation 3: _____________
Equation 4: _____________
Equation 5: _____________
Equation 6: _____________
Equation 7: _____________
Equation 8: _____________
Equation 9: _____________
Equation 10: _____________
Part 1
To get started, create the given picture on your
calculator:
Use the minimum equations necessary, because your
limited to the number of equations you can key into your
creativity will be
calculator…
Using this window:
one suggestion is:
one equation for y   x  3 and
another equation for y  x  3
How about another way?
Try: y   x  3 and reflect that over the x-axis
 f ( x ) which is y  x  3
but we could enter it in the calculator as y2   y1 t
another more efficient method is:
y =   x  3 uses one space for the two equations
Enter the  in calculator language as {1,-1}
I recommend saving your work often. Store the
picture to a graph database (GDB). This stores
 the graphing mode,
 window variables,
 format settings,
 all functions in the Y= editor and the
selection status of each and
 graph style for each Y= function.
To store as a GDB select
2nd Prog (Draw)
STO
3:StoreGDB
Assign a number from 0 to 9
Press Enter to store the current database to
the specified GDB variable.
To recall your GDB, select 4:RecallGDB from the
DRAW STO menu. Enter the number (from 0 to
9) of the GDB variable to which you stored the
graph database. Press Enter.
After you have saved, clear your y=
Your should have not graph….
Recall your GDB, and your graph and your
equations should come back!
Part 2
Start a new picture, with a clean graph.
Adjust the window so the circle will be round.
X to Y ratio must be close to 3:2
(zoom, decimal gets this window)
Next graph the circle (not a function!) ( x  3)2  ( y) 2  1
To enter it into the calculator, you need to solve for y…
So y   1  ( x  3) 2 would be
y  {1, 1}(
(1  ( x  3) 2 ))
Variations on circles are given below:
Notice I used transformations (or variations) of Y1
to save key strokes.
Save this as a different GDB.
Clear the graphs and we will try another picture.
Part 3
Using a basic circle: x 2  y 2  1 and variations, graph:
Choose your expression:
Write your equations in traditional form, change to y= if necessary
Key it efficiently into your calculator.
or
or ??
An example of a student project follows.
X to Y ratio in the window must be close to 3:2 or 1.5 so the circle will be round.
This one is 18:14 reduced to 9:7 approx 1.3 which is close enough.
As a class we compare this to the following rubric to help get a feel for what will be expected on your project.
*** Please note, your completed project must include a graph paper version and all equations with work
showing how you solved for y and labeled as to what part of the picture each equation represents.
There is no graph paper component,
so this project would lose 10 of the 30 points!
If you use the same shape in a different place, you may demonstrate your knowledge of shifting
functions instead of writing a new equation. (This would be considered a good thing and scored as a component
of “originality/difficulty” on the rubric).
Conics Project Grading Rubric
0
2006
1
Timeliness
Precision
Originality/
Difficulty
Variety of types
of equations -
more than
one major
error or 3
minor errors
boring
Follow directions
on paper version
Less than 4
types of
equations
no paper
components
Follow directions
on calculator
no calculator
components
Name __________________
2
1 day late
3
4
5
on time
3 minor
errors or 1
major error
2 minor
errors
1 minor error
below
average
average
above
average
4 types of
equations
All equations match
sketches, no stray
lines, intersections
appropriate
Well done!
3 parts
missing
2 parts
missing
1 part
missing
more than 4 types
of equations
Graphs on graph
paper
w/appropriate
window.
Equations labeled
with “picture part”
& type of equation.
Both traditional
form and “y=” form
of equations.
Saved with
equations, all parts
appear as on graph
paper.