Algebra 2
Name ____________________________ Date __________Per ____
CONIC SECTIONS PROJECT / TEST (With One Partner)
PARTNER: My partner is ___________________________________________.
TITLE OF OUR DRAWING: ______________________________________________.
OBJECTIVE: Create a picture that can be described by a series of equations of conic sections with restricted
domains.
GRAPHER: http://people.hofstra.edu/staff/steven_r_costenoble/Graf/Graf.html
BRING:
Your own laptop (optional) – bring at your own risk.
Graph paper (Ms. Yu has graph paper too) – this is useful for hand testing the equations.
1) You must have AT LEAST 20 EQUATIONS. These must include conic sections but can also include
linear, exponential, or trigonometric equations.
 at least 20 equations
2) Out of the 20 equations, 12 of your equations must be 3 of each different type of conic section (parabola,
hyperbola, ellipse, and circle) in your picture. For all conic sections except the circle, there must be at least
one vertical and one horizontal shape. Each partner must do at least 10 of the total equations and at least
1 of each conic section.
 Parabola – vertical
 Parabola – horizontal
 Parabola (any direction)
Initial: ___
Initial: ___
Initial: ___
 Hyperbola – horizontal
Initial: ___
 Hyperbola – vertical
Initial: ___
 Hyperbola (any direction) Initial: ___
 Ellipse – vertical
 Ellipse – horizontal
 Ellipse (any direction)
Initial: ___
Initial: ___
Initial: ___
 Circle
 Circle
 Circle
Initial: ___
Initial: ___
Initial: ___
 _________________
 _________________
 _________________
 _________________
Initial: ___
Initial: ___
Initial: ___
Initial: ___
 _________________
 _________________
 _________________
 _________________
Initial: ___
Initial: ___
Initial: ___
Initial: ___
This is just a check list. You can use more equations than the amount listed here.
3) DOMAIN RESTRICTIONS. At least 10 of your equations must have restricted domains.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
 Eq #___ has domain restrictions.
YOU ARE REQUIRED TO TURN IN:

1) This packet with the check list and initials.

2) Homework Equation Sheets – the equations that YOU did, solved for y by hand. It’s okay if
these are “rough draft” equations that you didn’t end up using. These equations must be different
than your partner’s.

3) Final Equation Sheets – the final equations the YOU did, solved for y step by step, hand
written or typed. These are YOUR half of the equations being used in the picture. These equations
must be different than your partner’s. Number the equations and these should correspond to the
same labeled numbers on the “Type into Grapher” Equation Sheet.
Include important information about conics:
Circles - center and radius.
Ellipses - center, x radius, and y radius.
Hyperbolas - center, x radius, y radius.
Parabolas - vertex

4) “Type into Grapher” Equation sheet - a list of ALL the equations used to create the picture in
the exact form in which they were typed into the computer, the shape requirement that they fulfill,
and the location in the picture. Number the equations on the sheet and on your print out. (Copy
and paste from your online file, and then label the equations.) You can your partner can print out
the same copy of this.

5) A print out of your graphed picture with the grid from the Grapher.

6) A large (at least 8.5” x 11” but no larger than 11” x 14”) copy of your picture carefully graphed
and colored or decorated to make an attractive picture. You may cut out your picture and paste it
onto a hand-drawn background. (ONE COPY SHARED IS OKAY.)
GRADING:
Projects will be graded on the equation and partner requirements above, creativity, difficulty, carefulness,
and accuracy. Neatness counts. You may type your math, but it is not required. Writing must be legible
and neat.
Creative design
/10
Decorative picture
/10
Careful graphing
/15
Accurate Equations
/15
Careful presentation
/15
Complete presentation
/15
Neatness
/10
Degree of difficulty
/10
Final Grade
/100
Creative Design
Innovative, not done before.
Careful choice to make maximum use of
limited graphing
Decorative Picture
Looks artistic, color, well presented
Careful graphing:
All lines intersect exactly where
appropriate. Lines and shares easily
included were not left out.
Scale and axes are present and square
Picture fills 8.5 by 11
Neatness
Orderly, clean, and tidy.
Neat handwriting or typed.
Accurate Equations
All included forms of equations and
restrictions are accurate.
Calculations of foci radii, centers,
focal points are accurate.
Careful Presentation
Readable, Sections are coherently
organized to facilitate analysis.
Carefully written or typed.
Complete presentation
All required elements are included.
Degree of Difficulty
How many equations were used.
Complexity of equations used
TIPS / FAQ (Frequently Asked Questions) – CONICS PROJECT
GRAPHER QUESTIONS:
1) What is the best way of typing equations into the Grapher and saving my equations?
1) Test each equation individually on the Grapher first.
2) When an equation works, save it in a word document. Separate each equation with a semicolon “ ; ”.
When you would like to test out a bunch, copy and paste all of them into the Grapher.
NOTE: If there is one mistake in the typing, the Grapher will not work.
NOTE: Your last equation cannot have “ ; ” after it.
3) At the end of the day, email and cut & paste the most updated equations back to yourself.
2) What if I only want to graph in Quadrant I (only positive numbers)?
Change your Min X, Max X, Min Y, Max Y to show only the boxes you want to see or zoom in to.
3) How do I count the boxes if Hosftra Grapher only shows the axes and intervals?
Put a piece of graph paper transparency on top of your print out and compare the boxes.
4) How do I print out my graph?
Press the “Print Screen” or “Prnt Scr” button. Then, go to Paint and paste. From there, print.
With the grids  don’t change anything
Without the grids  unclick “Show X/Y Ticks”
 unclick “Show X/Y Scale”
EQUATIONS, SHAPES, AND REQUIREMENTS QUESTIONS:
5) If I graph an entire ellipse/hyperbola/parabola and have to split it into 2 equations because it is not
a function, does that count as 1 equation or 2 equations?
Answer: 1 EQUATION.
6) How do I get weird shapes that we haven’t learned yet? Like diagonal parabolas?
Combine a bunch of known shapes together, using lots of domain restrictions. Or, look up in a math
book or the internet on how to graph diagonal conic sections.
7) How do I solve for y?
Look at your notes.
8) What counts as a domain restriction?
NO  half an ellipse, half a circle
YES  anything where you have to do “ … / (x>#smaller & x<#bigger)”
Example:
0;
(4/5)(25-x^2)^(1/2) ;
(1-(x-2)^2)^(1/2) ;
(1-(x+2)^2)^(1/2) ;
(3(x-13/2)^2-1) / (x>6 & x<7) ;
(3(x-15/2)^2-1) / (x>7 & x<8) ;
(3(x-17/2)^2-1) / (x>8 & x<9) ;
(3(x+13/2)^2-1) / (x>-7 & x<-6) ;
(3(x+15/2)^2-1) / (x>-8 & x<-7) ;
(3(x+17/2)^2-1) / (x>-9 & x<-8) ;
(3(1+x^2)^(1/2)-4) / (x>-3/4 & x<3/4)
Line  NO
Half ellipse (not a restricted domain)  NO
Half circle (not a restricted domain)  NO
Half circle (not a restricted domain)  NO
Parabola (restricted domain)  YES
Parabola (restricted domain)  YES
Parabola (restricted domain)  YES
Parabola (restricted domain)  YES
Parabola (restricted domain)  YES
Parabola (restricted domain)  YES
Half hyperbola (with restricted domain)  YES
ALG2 – CONICS PROJECT
Name __________________________ Date ____________ Per___
HOMEWORK EQUATIONS SHEET(S)
DAY #_____
SHAPE: ______________
Equation in Standard form:
Type into Grapher (include any
domain restrictions):
Sketch on x-y-axes:
Solve for y:
 Vertex: ________
 Center: ________
 Radius: _________
 Xradius: ____ yradius: ____
 Asymptote: _____
SHAPE: ______________
Equation in Standard form:
Type into Grapher (include any
domain restrictions):
Sketch on x-y-axes:
Solve for y:
 Vertex: ________
 Center: ________
 Radius: _________
 Xradius: ____ yradius: ____
 Asymptote: _____
SHAPE: ______________
Equation in Standard form:
Sketch on x-y-axes:
Solve for y:
 Vertex: ________
 Center: ________
 Radius: _________
 Xradius: ____ yradius: ____
 Asymptote: _____
Type into Grapher (include any
domain restrictions):
ALG2 – CONICS PROJECT
Name __________________________ Date ____________ Per___
HOMEWORK EQUATIONS SHEET(S)
DAY #_____
SHAPE: ______________
Equation in Standard form:
Type into Grapher (include any
domain restrictions):
Sketch on x-y-axes:
Solve for y:
 Vertex: ________
 Center: ________
 Radius: _________
 Xradius: ____ yradius: ____
 Asymptote: _____
SHAPE: ______________
Equation in Standard form:
Type into Grapher (include any
domain restrictions):
Sketch on x-y-axes:
Solve for y:
 Vertex: ________
 Center: ________
 Radius: _________
 Xradius: ____ yradius: ____
 Asymptote: _____
SHAPE: ______________
Equation in Standard form:
Sketch on x-y-axes:
Solve for y:
 Vertex: ________
 Center: ________
 Radius: _________
 Xradius: ____ yradius: ____
 Asymptote: _____
Type into Grapher (include any
domain restrictions):