Image Creation Using Equations

Introduction:

My project is making a picture using three types of functions. I am planning on using my textbook for background research and learning how to use functions. I will be using three types of functions, Linear, Quadratic, and Exponential. I have observed a few other projects and their outcomes, and have learned the simplicity of the shapes I will need to make.

Driving Question:

How do you make an image by using functions and graphing them?

Image Creation Using Equations:

The basis of my project is to make a still image using functions, using inequalities to limit the lines. The project materials needed are graphing paper, color pencils, and a graphing calculator.

SCIENTIFIC (MATHEMATICS) PRINCIPAL

Image Creation Using Equations displays how a series of equations is able to form an image. With a sufficient amount of equations an image will start to take shape.

Big picture:

The point of the project is to show that linear functions can be found in artwork.

Key words:

  • Function

  • Linear function

  • Quadratic function

  • Exponential function

  • Graph

Units:

  • cm2

Materials:

The materials that are required for this project are:

  • Graph paper

  • Pen/pencil

  • Textbook

  • Computer

  • Graphing Calculator

Procedures:

  1. Start with dividing your graph paper into four separate quadrants

  2. Use these functions to sketch out your picture.

  3. Make sure to check slope and coordinates in which the functions are located on the list.

  4. Use color pencils to color according to picture, located above.

Pictures:

PBL Investigation

Michael

HSA-Grand Prairie

1. How did you know which image would be good to do for this project?

I had to choose an image that would be slightly intricate, but simplistic enough to be made with simple lines. I chose the tiger because it is also the Mascot of Harmony Science Academy

2. Can functions create anything? How so?

Yes, I believe that with the utmost attention to design, Functions are able to create an infinite amount of designs.

3. What kind of functions did you use in this project? How did you decide those?

I used absolute value functions, constant functions, and linear functions. These are the functions with straight lines, allowing me to create the outline easier.

4. Did you use any linear functions? Why or why not?

I used linear functions to create the ears, nose, eyes, and stripes. They allowed me to have varying straight lines on different slopes.

5. Did you use any quadratic functions? Why or why not?

I did not include any quadratic functions, because they did not provide the closest resemblance to the base image.

6. Did you use any polynomial functions? Why or why not?

Polynomial functions were not sufficient or beneful to any area of my design. They did not replicate any of the areas of the original image.

7. Is your design symmetric according to any access? Why or why not?

Yes, My image can be replicated mirroring either side across the Y-axis. I have designed it this was specifically so the functions would be opposites of each other.

8. How did you decide the formula of the function?

I would use the simple y=mx+b for each section that was considered a line. I would then record the information on my worksheet.

9. How did you construct that formula?

The formula is already used in many algebraic studies and sections. With prior knowledge, I knew that it would be the equation most opportune to use

10. What was the most difficult part of this project? Explain.

The most difficult part of this project by far was finding the exact equations that were needed to replicate the image. I had to use the equation multiple times, just to make sure that the images and functions were coordinated

11. How would you describe your understandings of this project and how this is beneficial in

learning Algebra?

Learning various types of equations and functions is definitely beneficial in my understandings of algebra. Now that I can see how they may be used, I will be able to solve many problems faster and with a better grasp on the work I am doing.

Click here to download my PBL Investigation in Word Format

Click here to download my PBL Investigation in PDF Format