CONIC PROJECT Algebra H DUE DATE: Friday March 15, 013. This project is in place of a test. Projects are to be turned in during your period, handed to the teacher. Projects may be turned in early (They must be handed to the teacher). Projects must be turned in on time to receive full credit. Student absence or tardiness will mark projects as LATE. o FOR ANY CONSIDERATION REGARDING EXCEPTIONS TO THE DEADLINE, CONTACT THE TEACHER BEFORE THE DEADLINE; THIS DOES NOT GUARANTEE AN EXTENSION WILL BE o MADE. Projects turned in after your class period on Friday 3/15/13 but by on Monday, March 18 th will be accepted, but docked 0 points. o Projects will not be accepted after 3/18/13. This is a group project with either 3 or 4 members per group. Once a group has been formed, it may not dissolve any members without the consent of the teacher. o o Group assignments affect the grade of all members in the group Individual assignments only affect the grade of the individual GOALS: Investigate the graphs and equations of conic sections. Use these equations to create designs and investigate planetary orbits. GRADING: This Project is worth 100 points. Grading is based on accuracy, neatness, completeness, grammar, and spelling. THE PROJECT: Consists of 15 assignments, listed below, including your notes from the chapter. They are to: Be neatly arranged in a 0.5 3-Ring Binder in the order listed. No folders or staples. Papers are NOT included in sheet protectors. Include a Table of Contents. Individual pages do not need to be numbered. Include a title page/cover sheet with names, period, and date. Be clearly labeled with a student name for each assignment labeled with a * WRITING ASSIGNMENTS: Here are the directions for the assignments involving writing. These are the assignments that must be typed and printed. Cover Sheet / Title Page Table of Contents Planet and Scientist Report Calculator Use Paper These are the directions for the typed assignments. Failure to follow these exact directions may not earn full credit. Margins on all sides of the page must be 1.00 Font set must be Arial or Times New Roman Font size must be 1 point The typing must be double spaced For the Calculator Use Paper, only list the title at the top of the page. Do not include member names, dates, periods, etc. Essentially, your paper must begin on the second line.
THE ASSIGNMENTS: Here are the assignments. Submit in this order. 1. Grading Sheet: Write the name of each group member on the grading sheet.. Cover Sheet / Title Page (Names, period, date) 3. Table of Contents 4. Standard Form Conics: For each of the following (EACH LETTER MUST BE DONE ON A SEPARATE SHEET OF GRAPH PAPER): Name the conic each Standard Form represents Show a graph centered at the origin and at least two transformed graphs, with equations Write at least 5 complete sentences comparing the graphs and explaining how changes in the equation change the graph A) D) ( x h) ( y k) r B) ( x h) ( y k) a b 1 E) x a( y k) h C) ( x h) ( y k) a b 1 y a( x h) k ( y h) ( x k) F) a b 5. General Form Conics: Classify each conic and write in vertex/center form. Draw an accurate graph. Name the important features of each graph. Write the coordinates of the vertices & center. This assignment must be done on GRAPH PAPER. A) 9x 4y 36x 16y 164 0 B) 15x 15y 150x 30y 330 0 C) 16x y 160x y 505 0 D) y 16x 14y 17 0 6. a. Planet Report: Choose a planet (Sign up with your teacher). Then complete the Planet Report sheet. b. Scientist Report: This must be typed. 7. Real World Conics Worksheet 8. Systems of Conics: Find the points, if any, that the graphs of all the equations in the system have in common. You may round your answers to 3 decimal places. On GRAPH PAPER, draw an accurate graph for each. Write the coordinates of any intersection point(s) on the graphs. x 3y 4 A) y x D) x y 8x 0 x 5y 4x 5 0 x 3y 19 B) x y 9 E) x y 4x 4y 6 x y 4x 54 y 3x 8 C) x x 1 y 16 y 4 9. Calculator Use Paper: Write a 400 word minimum paper on Calculator Use in the High School Classroom. Include quotes from all group members and at least three adults (parents, other math teacher, sibling studying math/science in college, etc). Include if/how using a graphing calculator has changed how you do math and how the graphing calculator helps or does not help you learn math. Include comments on whether math classes should or should not include both paper and pencil learning as well as graphing calculator learning. This must be typed. 10. *SNOWMAN 11. *HAPPY FACE 1. *INSECT 13. *Pg. 558: 1, a, c, d, 3 6, 1, 14 You must use GRAPH PAPER 14. *Design Project: Using a graphing calculator, create and name a design. Print your design using a computer and printer. ALSO INCLUDE: 15. *Notes you took during the chapter (You will get these back) ORDER: Submit 1-9 in order. Then include assignments 10-14 from Person 1, then 10-14 of Person, etc. Finally, include each person's notes, in the same order as assignments 10-14.
PLANET AND SCIENTIST REPORT PLANET REPORT 1. This report requires both an accurately hand drawn graph and a written report.. To draw the graph, do the following: a. Find both the shortest and longest distance (in kilometers) from the sun to the planet you chose. http://www.windowsuniverse.org/kids_space/distance.html b. The sun is one of two focus points (equidistant from the center along the major axis) inside the elliptical orbit of your planet. Use the following information and your notes to find values for a, b, c and then the equation of your planet s path through space. i. C is the distance from the center to a focus point. ii. The sun is one of the focus points. iii. a is the entire length of the ellipse through the center and both foci. iv. b is the entire width of the ellipse through the center. v. The longest distance = a + c. vi. The shortest distance = a c. vii. a b c c. Write an equation in standard form for the orbit of your planet. You must show supporting work to show how you found a and b. 3. Draw an accurate graph of your planet s orbit on a full-sized sheet of graph paper. Write the scale & units on your graph. Label the coordinates of the sun and the center on your graph. 4. Write a minimum 10 sentences, telling interesting facts about your planet. You must list the resources that you used. WIKIPEDIA (or any other virtual encyclopedia) may not be listed as a resource. MUST BE TYPED SCIENTIST REPORT Choose a scientist from the list below and write an interview which includes a minimum of 10 questions and accurate answers. You must include his/her connection to astronomy and/or mathematics and/or conics. A column format is acceptable. You must list the resources you used. WIKIPEDIA may not be used as a resource (Though the citations Wikipedia uses may be of use). MUST BE TYPED Edmund Halley Tycho Brahe Johannes Keplar Apollonius of Perga
REAL WORLD CONICS Write your answers and supporting work on graph paper. You must show supporting work for your answers. 1. Statuary Hall is an elliptical room in the United States Capitol in Washington, D.C. The room is 46 feet wide and 96 feet long. Because of a reflective property of an ellipse, a person standing at one focus can hear even a whisper spoken by a person standing at the other focus. (John Quincy Adams is said to have used this feature of the room to overhear conversations.) a. Find an equation of the ellipse b. How far apart are the two foci?. An irrigation project in Libya enables farmers to raise crops in the desert. Water from deep wells is pumped to sprinklers that rotate in circular patterns. Each circular field has an area of about,400,000 square yards. Write an equation that represents the boundary of one of the fields. Let (0,0) represent the center. 3. Most communications satellites have synchronous orbits, which mean they circle the earth at exactly the same speed as Earth is rotating. For a viewer on Earth, such a satellite appears to be stationary. Find an equation that represents the circular orbit of a satellite placed,40 miles above Earth. Let (0,0) represent the center. (The circumference of Earth is about 5,000 miles.) 4. LORAN (long distance radio navigation) uses synchronized pulses sent out by pairs of transmitting stations. By calculating the difference in the times of arrival of the pulses from two stations, the LORAN equipment locates the ship on a hyperbola. By dong the same thing with a second pair of stations, the ship s location will be the intersection of two hyperbolas. LORAN equipment has calculated a ship s position to be the point of intersection of the graphs of the following hyperbolas. Find the coordinates of the point of intersection. Draw an accurate xy 4 0 graph. x 5y 100 0 5. In Australia, football (or rugby) is played on elliptical fields. The field can be a maximum of 170 yards wide and a maximum of 00 yards long. Let the center of the field of maximum size be represented by the point (0, 85). Write an equation of the ellipse that represents this field. The area of an ellipse is A ab. Find the area of the field. Draw an accurate graph. 6. You are opening a restaurant called the Treetop Restaurant. The menu cover has a tree on it. You are using a computer program to design the menu cover. The equation for the tree trunk is 100x 9y 36y 900 0. Write this equation in standard from and y form and then draw an accurate graph. 7. The following is an equation of a comet s path. Tell what type of path the comet follows and draw an accurate graph of the comet s path. The sun is inside the path a distance of p units from the vertex, where p = (coefficient of the non-squared variable)/(4*coefficient of the squared term). Will this comet pass by the sun more than once? Explain how you know. 3550x 1400x 7100y 13050 0
SNOWMAN, HAPPY FACE, INSECT For each shape, in addition to the instructions given, Hand-drawn accurate drawing on a full-size sheet of graph paper. Your picture should reasonably take up the entire page Complete a Conics Equation Chart Use the same scale (either 1 or ) on both axes Each equation must be a function (vertical lines are acceptable) Each picture must have a minimum of 10 equations SNOWMAN 1. 3 circles (one for each snowball). Additional features (i.e. nose, arms, buttons, hat, scarf, etc.) ELLIPTICAL HAPPY FACE 1. Ellipse for face. additional complete ellipses for facial features (i.e. eyes, nose, mouth, etc.) 3. At least additional features your choice of equations INSECT 1. Ellipse for the body. Circle for the head 3. Hyperbola for 1st set of legs 4. Parabolas for the nd set of legs 5. Use (, -1) as the center of the body 6. At least 1 additional feature your choice of equations
CONIC EQUATIONS CHART (CEC) Name: Title of Picture: Feature or Graph Number Equation in Standard Form Equation in y Format Domain Range
DESIGN PROJECT 1. You will create a design on your calculator. You must use all four conic sections at least once. The design should be aesthetically pleasing; a random hodgepodge of four conic sections will not earn full credit.. Print your design and program code using a GraphLink/TI-Connect and a computer. 3. Transfer your design to the teacher's calculator How to Program on Your Calculator Press the [PRGM] button on your calculator. Select [NEW] to create a new program. NAME: Type your last name. With any spaces remaining, type your first name. o Example: If I was creating the program, it would be SCOTTCHA 1 st line of Program: ClrDraw ( [ nd ] [PRGM] 1: ClrDraw ) This clears any pictures or other graphs already in your graphing window. nd line of Program: AxesOff ( [ nd ] [ZOOM] AxesOff ) This removes your axes from appearing when the picture is drawn. 3 rd line of Program: FnOff ( [VARS] [Y-VARS] 4: On/Off : FnOff ) Turns off any equations in the y menu 4 th line of Program: PlotsOff ( [ nd ] [Y=] 4: PlotsOff ) Turns off any Stat Plots. OMIT this line if your graph uses the stat plots Set your window. Type the number you want for the minimum and maximum values for x and y Should be of the form: -3.5 xmin 3.5 xmax -15.5 ymin 15.5 ymax xmin, xmax, ymin, and ymax can be found by pressing [VARS] 1: Window Note that the " " is the arrow found by pressing the [STO] button on the calculator You may use any window you want, but you should have the x : y ratio close to 3 : Enter equations by pressing [ nd ] [PRGM] 6: DrawF( Restrict domains by pressing the divide button and then using the TEST Menu ([ nd ] [MATH]) For example :DrawF x / x 3 and x 5 Use [CLEAR] to delete an entire line Use [ nd ] [DEL] to insert a blank line You can shade if desired by pressing [ nd ] [PRGM] 7: Shade :Shade(F 1, F, x 1, x, #) F 1 : Bottom function where shading begins F : Top function where shading ends x 1, x : Starting and ending domain values to shade #: A number from 1 to 8, where 1 is the darkest shade I have found that this does usually does not work very well Printing the Graph Run the program and get the image on your calculator Connect your calculator to a computer using a Link Cable Open TI-Connect Choose Screenshot from the main menu Take a screenshot of the calculator to print IMAGE RESIZE 300% Print the image Printing the Code You may not screen capture the code from the calculator; it must be neatly typed You will need to type your computer code into a word processor and print it
Conics Project Grading Sheet Period: Put names in alphabetical order, according to last name. Assignment Group Title Page Minus pts Neatness, Minus Presentation pts 1. Graph 1 Investigation each. Classify conics 1 3 each 3. a) Planet 6 Orbit Report resources b) Scientist 5 resources 4. Real World 10 5. Systems 15 3 each 6. Calculator Use 5 7. *Snowman 5 8. *Happy Face 5 9. *Insect 5 10. *P. 558 5 11. *Design 10 1. *Notes 5 Grading Sheet Group Total 65 35 TOTAL/100 ** **