Name: ______Date: ______Period: ______
Quadratic Functions Project: Parabolas Everywhere
Objective: Why are we assigning this to you?
1) To recognize and identify parabolas in everyday life. What are their general characteristics? How easy are they to spot?
2) To model objects with parabolic shape with quadratic equations.
3) To use the model to make predictions.
Instructions: What you have to do!
1.) Decorate the given Spartan head. This Spartan head must have your initials incorporated into the decoration.
2.) Find 3 examples of the graph of a quadratic function with a camera.
a. Your photos must have your decorated Spartan head in one corner so I know you took the photo. (make sure the Spartan head doesn’t cover the parabola!!)
b. Each photo must be unique – no duplicates.
c. Make sure the parabola is not at an angle when you are photographing!
d. Print out all 3 pictures with Spartan Head in one corner of the picture.
e.
3.) Determine which of your parabolas is best modeled by a quadratic equation. For each of your photos overlay a coordinate graph system over the picture using Desmos (www.desmos.com). I will post a video on my website for you to watch that explains how to do this.
a. Choose a position for the parabola that allows you to get five coordinate points that lie on your parabola.
b. Identify the five coordinate points. Graph these points in Desmos.
c. Run a quadratic regression on these points in your graphing calculator. Write down the regression equation and the R2 (coefficient of determination).
d. Put your screen in projector mode.
e. Enter the quadratic regression equation into Desmos.
f. Save & print out your 3 graphs with Desmos overlay.
4.) Determine which method is best at modeling your parabola and predicting points. Using ONLY the picture of the parabola that has the highest R2 value (closest to 1.0).
a. Standard Form using Quadratic Regression.
i. Choose an integer x-value that is not one of the five previously picked points.
ii. Plug it into the regression equation to get the y-coordinate. Plot this point into Desmos. This should lay directly on or close to your parabola.
b. Vertex Form. Position the vertex on a non-zero, integer coordinate, that also allows you to identify another point on the parabola that is also composed of integers.
i. Identify the (h,k) and other point being used, then graph these points in Desmos.
ii. Derive the quadratic equation in vertex form. Enter the equation in Desmos (one color)
iii. Rewrite in standard form. (show your work). Enter the equation into Desmos (this should lay directly on top of your parabola from standard form if you have calculated it correctly.)
iv. Use quadratic formula to predict the x-intercepts. Graph these points in Desmos.
v. Using interval notation describe the Domain, Range, increasing interval and decreasing interval.
c. Intercept Form. Reposition the graph so that you have two x-intercepts that are integers.
i. Identify the x-intercepts and one other point, then graph these points in Desmos.
ii. Derive the quadratic equation in intercept form. Enter the equation in Desmos (one color)
iii. Rewrite in standard form. (show steps). Enter the equation into Desmos (another color)
iv. Use the equation in standard form to calculate the points of the vertex. Graph these points in Desmos.
5.) Report
Format of report should be as follows:
1. Copy of Rubric with name, block and presentation information filled in.
2. Introductory paragraph that covers the objectives of this project.
3. Description of photographs paragraph. For each photograph..
a. Describe the where, when and why (or interesting fact)
b. Describe the opening (concave up or down) and width (stretch or shrink) in comparison to the parent function.
c. Identify the R2 value, then based on this choose which picture you are going to further analyze.
4. Summary of calculations
a. Give a summary of data found using the vertex form including equation in vertex form, rewritten equation in standard form, intercepts from quadratic formula and comparison to actual intercepts on graph.
b. Give a summary of data found using intercept form including equation, rewritten equation in standard form, calculated vertex and comparison to actual vertex on graph.
c. Give a summary of regression analysis including the equation in standard form, the predicted point using the equation compared to the actual position on your parabola.
5. Conclusion – discuss how you were able to meet all of the objectives of this project. How good were you at recognizing parabolas? Back your statement up with R2 values. Explain how you know how to model parabolas now? Which method do you think is the best method to use to make predictions and why?
6. Attach supporting pictures and calculations in the following order:
a. 3 original parabola pictures
b. 3 original parabola pictures superimposed in Desmos with regression
c. Calculations for vertex form
d. Calculations for intercept form
6.) Presentation – You can create the presentation individually or in groups up to four. Be creative and
come up with a type of presentation that embodies the spirit of the project. Choose one of the following formats.
a. Artwork – create a unique piece of artwork that includes parabolas. (individual only)
b. Video – documentary, movie trailer about parabolas, skit, song, video
c. Classic Presentation – Powerpoint or Poster that details your process and findings of your
report
Other information:
· Almost all of the work will be completed outside of school. You will have one day in class to work on it.
· The report part of this project is to be completed independently. No two students can use the same picture.
Project Timeline
· 11/9-11/10: Project Assigned
· 11/28-11/29: Steps 1 & 2 of instructions completed. Bring hard copy of 3 pictures to class.
· 12/16-12/19: Step 3 of instructions completed. Bring Desmos print-out of all 3 photos.
· 12/20-12/21: Work in class on equations
· 1/11 - 1/12: Report Due
· 1/24- 1/25: Presentations Due
Name: ______Block: ______
Rubric for Quadratic Functions Project: Parabolas Everywhere
Presentation Type:______Members of Presentation Group: ______
Use this rubric as a “checklist” to help you as you complete your project. It will also be used to score your entire project on the final due date.
Criteria / Points possible / Points earned / Due Dates3 original pictures of parabolas, without the coordinate plane included. / 2 pts/each / 11/28 – 11/29
Regression Calculations and Graphs
- A coordinate graph was accurately imported into Desmos over a copy of 1 parabola with 5 points identified and regression equation modeled.
-Write the regression equation in standard form
-Write the R2 (coefficient of determination) / 3pts/photo
2pts/photo
1pt/photo / 12/16 – 12/19
Desmos graph superimposed onto photo with the following:
*vertex plotted at non-zero integers.
*extra integer point
*graph of the equation (vertex form)
*predicted x-intercepts
Calculations (SHOW ALL WORK!!)
*Identify the (h,k) and additional point
* Estimate the equation of the parabola
using vertex form
*Rewrite the equation in Standard Form
*Calculate the x-intercepts.
* Domain, Range, inc. & dec. intervals / 7
2
5
3
5
4 / 12/20 – 12/21
Desmos graph superimposed onto photo with the following:
*x-intercepts plotted at integers.
*extra integer point
*graph of equation (intercept form)
*predicted vertex
Calculations (SHOW ALL WORK!!)
*Identify the x-intercepts and additional point.
*Estimate the equation of the parabola using
intercept form.
*Rewrite the equation in Standard Form
*Calculate the vertex / 5
2
5
3
5 / 12/20 – 12/21
Report
-Introductory paragraph
-Description of parabolas paragraph
-Summary of calculations (Vertex, Intercept, Regression) 2pts/each
-Conclusion Paragraph /
4
6
6
5 / 1/11 – 1/12
Presentation
Clear, neat and creative presentation that includes information inspired by the information above / 10 / 1/24 – 1/25
Total / 100 points