DESMOS Drawing!

https://www.desmos.com/calculator/asll5riedc


When this assignment was given to me, I was so excited to begin. At first, I had no idea what I wanted to create. My greatest option was to just browse the internet, and so I stumbled upon this image:

Related image

It gave an edgy aesthetic, which I kind of liked. The first thing I noticed was that it had a lot of short lines used for eyebrow and eyelash details. I decided that it would take way too long to create every line, so the idea of inequalities was brought to my attention. My plan was to shade in the eyebrow regions as well as the eyeliner regions. After planning out the general final look of this project, I started graphing on DESMOS. The first thing that I did was make the frames of the eyes. I did this step first because the frames of the eyes shape the entire look, so I had to get this step right. My next step was to graph the eyeballs. To be honest, I had trouble figuring this part out. I required assistance from Mr. Salisbury when I realized I didn’t know how to graph translations for the circles. I also struggled with setting the correct restrictions on the circles so they fit inside the eye frames. In the end. the solution was to graph the exact same circle twice and set two different restrictions so they overlap. That was my main challenge during the graphing process.

For my drawing, I used quadratic equations the most. This is most likely because my image consisted of many eyelashes and generally “round” lines. Quadratic equations were the easiest to use because their curves could be easily altered to fit the drawing I was going for. The second most used equation would probably be the linear equation. Although it may seem like my drawing doesn’t include many (if any) straight lines, it actually needed many short straight lines to connect the curved lines. The linear equation, much like the quadratic equation, was easy to manipulate, since the equation itself is simple to understand. Lastly, another equation – actually, relation – that I used quite a bit was the circle relation. Like I mentioned previously, I used it when graphing the eyeballs. However, it also came in handy when making curves that circled more than 180 degrees, which was difficult to do without graphing circles. Other than these equations (and relation), I also used a couple of trig functions and reciprocal functions. These were only useful in certain situations; for example, I used the reciprocal function for the nose and the trig function for a lip. This was simply because these functions perfectly captured the curves that I was trying to achieve for these specific features. Unfortunately, I did not get around to using cubic equations, square root functions, or exponential functions.

As I learned from Pre-Calculus 11, translations were graphed by adjusting the p and variables in the quadratic equation. I became very nit-picky with the translations, as each line had to be perfectly aligned with one another. All of my equations had numbers like “2.7384” going all the way into the ten thousandths to make sure it was precisely graphed. This was also the case for vertical or horizontal extensions or compressions. Eyelashes took a long time because I tried to get each eyelash parabola compressed or extended to a perfect degree. With graphing, I did not really use any strategies, unless you count copy and pasting a strategy. When graphing many lines that were similar, like eyelashes per se, I would copy and paste one equation over and over and then simply alter that one equation. This reduced a ton of time for me.

desmos

Just for fun, I decided to add on to my original image plan and create a nose and mouth. This was just an impulse decision, and I completely eye-balled the entire thing. (I believe I forgot to mention this earlier, but I also technically eye-balled the eyes as well, because I was dumb and didn’t know I could paste my image into DESMOS and use it as a guide.) Either way, it was very fun to graph on an online program for the first time. The process was so engaging that every time I began to graph, I wanted to continue even after the class was over. I learned/reviewed how to translate graphs, compress/stretch circles, use inequalities to shade in areas, and use restrictions to determine where lines begin and end. This project was an extraordinary and awesome way to end our math year. I genuinely enjoyed learning how to graph images on DESMOS, and I might continue creating fun graphs and exploring the possibilities of functions and equations.

Math Art with Functions!

The link to my rendition of Mike Wazowski doing the sine function dance: https://www.desmos.com/calculator/cxicbkswjz

screen-shot-2019-06-09-at-10-05-29-pm

 

 

For this project, I decided to choose Mike Wazowski. I drew inspiration from childhood movie characters and thought Mike would be a fun challenge. I loved his monster appearance and also knew that creating him would require the use of several different functions. I chose not to use an image so I could fully recreate Mike with my own style, meaning I could modify certain aspects of his appearance to fit my liking and to employ the use of a variety of graphs.

Functions used:

Circle function of form  x2 + y2 = r2

Rational function of form x^2 + 2 / x – a rational function uses polynomials in the numerator and denominator – represented as rational fraction

Square root function of form  f(x)=√x

Quadratic function of form y = ax2 + bx + c,

Exponential function of form y = abx

Linear function of form y=mx+b

Sine function of form y=sinx

My strategy is as follows:

First, I wanted to create the main shapes and outlines of his body. I knew that creating the larger shapes ar first would allow me to set some boundaries for the smaller details within his face and arms. I began with the head, which was a simple circle function. I discovered that manipulating the radius would allow me to modify the size of the head. I positioned the head in the middle of the graph about the origin to make future reflections easier, adding values to the x and y values as needed. After creating the head, I moved on the outer outline of his eyeball. I used another circle function with a smaller radius. I then used an inequality to shade in his iris, then proceeded to manipulate the coefficients to create the pupil. I discovered that the coefficients modified the length and width of the circle, meaning that I could also make it an oval.

To make the horns, I used rational functions rather than using quadratic functions. I knew rational functions would give me a softer curve, and I wanted to experiment with using an unconventional function. I added a coefficient to the input within the function in order to perform a horizontal compression. To reflect the horn on the other side of the head, I used a negative reflection of the y-axis by adding a negative sign to the input. I then added restrictions

Now onto the arms (part 1). Though his arms were quite linear and straight in the movie, I wanted to make a realistic arm that was somewhat curved. To do this, I used square root functions to make the bottom half of his arms. I added a coefficient to the input to make his arm the steepness I wanted it to be, using a horizontal compression. I then subtracted a constant from the entirety of the function, vertically shifting the bottom line of his arm to the position I wanted it to be on his body. To create the second line above the bottom line, I manipulated the vertical shift so it would be higher than the previous lines. To make things simple, I reflected both these lines to the other side of his body and used the necessary restrictions.

The elbows were an interesting, albeit ridiculous addition. To make Mike even more lifelike, I wanted to give him monstrous, pointy elbows. I used quadratic equations, as they produce parabolas with vertexes/points. I added a coefficient of 13 to the input to horizontally compress the parabolas. I then reflected the elbow to the other side and used inequalities to shade them in.

The second part of the arms were simple linear equations. I modified the y-intercept to create parallel lines above the initial lines I created. To add the same arms to both sides of his body, I reflected across the y-axis. For his hands, I also used quadratic functions.

For Mike’s legs, I used exponential functions, knowing they have a long, sweeping curve. I didn’t want to repeat the arms process again for the legs, although they are straight in the movie. I wanted to experiment with exponential functions and their potential to create even creepier legs. The first line was relatively straight, but the lower part of the leg needed to be curvier, so I manipulated the number and power in front of the input (which in this case, lies in the exponent). I reflected the leg across the y-axis. I used inequalities to shade this area in, but it was difficult to shade the entirety of the leg in with inequalities without the inequality not covering a certain section or extending too far into his head. For his feet, I used a quadratic equation (not function) by switching the inputs and outputs in the quadratic equation to make it sideways. I reflected this across the y-axis to create both feet.

In order to make the smile, I knew I could restrict a sine function to use its curve/dips. I inputted a sine function and restricted the x value so I ended up with a portion of the function. For the upper line of the smile, I used a quadratic function with a small slope in order to make it flat. Creating the teeth was a painful process. I used a large number of linear functions, creating new lines by manipulating the slopes from positive to negative repeatedly to create triangles and restricting them as needed.

Just for fun, I added a blue hat (representation of his MonstersU hat) and rainbow eyelashes. I liked the creative freedom of not using a reference photo. For the eyelashes, I used linear equations. For the hat, I used a quadratic equation.

This project was a challenging but rewardable experience. The hardest aspect was making sure small details of the lines were neat and positioned at the right places. Shading the arm was also incredibly difficult, as I had to use individual inequalities for the elbows and different sections of the arm to shade in the arm as much as I could. I loved the experimentation process and discovering how manipulating values would change the shapes of graphs. These skills will undoubtedly help me in future math classes. I improved my ability to visualize mathematical functions and the relationship between an equation and its visual image.

Desmos graph art

https://www.desmos.com/calculator/hqf7bmrhp5

My approach to this project was very much trial and error. Though I had a general idea of what I wanted to create, I used multiple smaller images and some free-handed work to complete the design. After about a class and a half, I managed to start completing transformations of graphs with little to no thought as I relaxed into the patterns. The most challenging aspect of this project was finding equations that fit some of the lines I wanted to draw. I had to scrap a couple of ideas that just couldn’t be drawn with my knowledge of functions and equations. However, despite this, I am happy with my end result and I really enjoyed the project overall. Being able to experiment and try new techniques on Desmos helped me to develop a comprehensive understanding of transformations, while still completing a really enjoyable project. :)

little lady – DesmosPortraitMath10FPC2019

Take a look at the little lady.

For my art piece, I chose a portrait of a little lady. In the beginning, I was only looking for an aesthetic picture, so there wasn’t much thought concerning the difficulty and sophistication of the image. I only realized that I had chosen a picture that had a lot of small details after I began. So, without a plan, I just charged into this project headfirst.

The first part I decided to do was the Collar Texture (you’ll see it labelled so), because it was relatively simple. It consisted of straight lines, so all I used were linear equations and functions. This was simple, although time-consuming, and allowed me to get into the groove of adjusting different values, such as slope.

The next part I decided to work on was the Collar Lace. I used circles for the majority of the lace because all of the lines were curved. Circles were also very simple to manipulate, but I had to make a lot of them! Over time, I realized that it was easier to copy and paste similar looking lines and adjust them accordingly, which made my work more efficient. In order to match the lace with the circles I had created, I used a lot of circles for just one line, which made the Collar Lace take a long time.

Afterwards, I worked on the rest of the Clothing. I used exponential, quadratic, square root, and linear functions, as well as circles. The lines for the Clothing weren’t as curved, so I had to make the decision of whether I wanted to use circles or not. After experimenting with different graphs, I decided on the functions depending on how similar they looked to the line in comparison. Sometimes, if the result was dissatisfactory, I simply tried a different graph.

The Face and Neck were the next areas I focused on. The Face and Neck were a lot simpler than the earlier parts, as there were fewer lines. I used a combination of reciprocal, quadratic, and linear functions, as well as circles. The only trouble I ran into concerned linear equations. It was a struggle to make sure I had the correct slope because I would often have to adjust the slope number by number.

Next came the Hair. The Hair was similar to the Collar Lace. I used reciprocal, quadratic and linear functions, as well as circles, to create the Hair. Similar to the Collar Lace, there were lots of curved lines. Luckily, the Hair had very similar lines within itself, so once I had finished layering a line, I would copy and paste the functions and adjust accordingly, which saved me a lot of time.

Finally, I had to do the Eyebrow and the Eye. The Eyebrow and the Eye were simple. There were few lines, and after working on the rest of the drawing, I had a good idea of what I was doing. I used linear and quadratic functions, as well as circles. However, when I began to use inequalities in order to shade the Eye and the Eyebrow, it began to become confusing. It was simple to shade the initial region, but the real challenge came with setting limits. After experimenting, I realized that a lot of what I had done resulted in the ‘!’ mark, motioning that my inputs were not applicable. After struggling for a while, I wondered, why not put the entire function as a limit within brackets? I was just trying something out, without much hope that it would be successful. Luckily, it worked, and I was able to apply it to the rest of the regions I had to shade. (Refer to Eye and Eyebrow- Inequalities)

Throughout this project, I didn’t feel the need to ask for help, although I was asked by my tablemates to help out sometimes! I got through the majority of my problems by experimenting and testing out things I thought would work or were interesting. After a lot of experimenting, I came to understand that even though different types of functions have diverse results, manipulating functions is predictable and consistent. For example, adjusting ‘y’ within a bracket makes the entire function move vertically because, with the addition of the new value, the value of ‘y’ must adjust itself to maintain, essentially, the value of zero within the bracket. Same with manipulating ‘x’ within a bracket. Something intriguing I learned was that switching the positions of ‘x’ and ‘y’ causes the function to be reflected diagonally, I’m going to assume, along the line created by ‘y=x’ in a square root equation (refer to Clothing- the second equation). In addition, I learned that with inequalities, if I want the region shaded to be limited by another function, I can input that equation into another set of brackets as a limit itself, after changing it into an inequality by changing the ‘=’ sign to an inequality, such as ‘<‘ or ‘>’.

Overall, this project brought lots of joy and was surprisingly relaxing. I might go as far as to say that it was therapeutic! I understand the nature of functions a lot better and how different coefficients and values affect the way a function moves. Even though a lot of concepts were covered in Math 11 already, I was able to deepen my understanding. This project was an opportunity to apply the knowledge I had gained and perhaps, I will begin to draw on Desmos as a stress-relief technique! :))))

Desmos Graph

link to graph

Over the course of the past week, I created my own math version of Kermit the Frog on Desmos. I chose to do Kermit because I wanted to an image that had defined lines but also with a level of challenge. The image of Kermit I choose had a lot of curved lines but also was two dimensional meaning that I could still complete it within the given time frame and my level of expertise. The biggest challenge I ran into was finding a way to use functions to do curves that were a little irregular. At the beginning, I wanted to do a parabola that was rotated 90 degrees and no matter how many numbers I changed the equation y=x^2 wouldn’t work. However, two days later, I accidentally punched in x=y^2 and found that the parabola rotated. This might not be the most mathematically ‘aha’ moment, but as soon as I punched it in, I realized how simple the solution is. I used this equation a lot in the future.

Another challenge I came across was not knowing where to start. I wanted to start somewhere easy but I realized making art out of math isn’t exactly the easiest thing. As I continued with this project, I found out it’s only gets easier as I start to work on it more. I learned through experience and found different ways to create curved lines and how to create restrictions that helped me build the image. I tried to do inequalities over the weekend, but no matter how I moved it, as soon as I zoomed out the inequality would disappear so I took them out. This is definitely something I want to figure out how to fix in the future. As well as, when I first started, I couldn’t seem to get the lines to match up at all. After asking around, I found out that if I put my curser on the line, it tells me the exact points to the third decimal and that helped a lot. This seems really small but it made the rest of my project smoother.

And so to the actual functions I used:

Quadratic Equation: y=x^2 OR x=y^2

I primarily used this function because this allowed me to make curves big and small as well as create a loop at the bottom that I used on features like the side of Kermit’s face and the curved edges on his hand. I mainly stretched the parabola to make it larger. I also used horizontal and vertical translations and reflections to move it to the spot that I wanted it to be.

Square Root Function: y=squareroot x OR x=squareroot y

I used this function when I needed a slight subtle curve; for example on his forearms. I used translations left and right to get it to the spot I desired as well as stretching and compressing to get it to be the size that I wanted it to be.

Reciprocal function: y=1/x

I used this function for more prominent large curves such as his mouth.

Linear Equation: y=mx+b

I used this equation to connect all the curves together. The image I chose wasn’t facing forward; the entire image was a little tilted so I used a straight line to connect multiple curves that wouldn’t quite fit together. I changed the slopes and the intercepts to get it where I want.

Circle: x^2+y^2=r^2

Although this is a relation and not a function, I used this equation a lot. I used it for the eyes and to make curves that I couldn’t quite make with the other equations. I used restrictions (both x and y restrictions) to cut it to the curve that I wanted.

Through this project, I learned a lot about graphing and functions but I think I do need to study them a bit more even though I made nearly a hundred of them. For the majority of this project, I would input the equation I wanted and then fiddle with the numbers until it fit. This project helped me wrap my mind around the concept but I need to apply this new knowledge on smaller, relevant numbers.

surprised patrick star

https://www.desmos.com/calculator/s6qdwrlqye

These were the equations I used throughout my graphing process:

Quadratic and reciprocal functions were used because of the slight curve they provided. A cubic equation was used on the weird occasion regarding the curves in his pants, to get a softer curve. These were specific to the outline of the bodies, mostly used because they were easy to shape. When moving these equations, I would place the variables within brackets, subtracting or adding numbers from the y variable in order to move them vertically. When moving them horizontally, I subtracted or added outside of the squared equation, essentially changing the overall value, moving it farther down the x axis.

The circle equations were used for objects like Patrick’s eyeballs and stomach. To make the circle smaller or larger, I input numbers into the r variable. In order to move them vertically and horizontally, I did the same thing, placing the variables within brackets and subtracting or adding.

Linear equations were used for the straight line which were simpler. I placed coefficients in front of the x variable in order to change his angle, subtracting or adding to change the x axis like the other equations.

I didn’t face any real challenges, other than wanting to work around images and instead go off of what I could see. As for “aha moments,” there was one early on, when working with the placement of a circle. When creating Patrick’s eyes, I had no clue as to how I would change the circles x and y, specifically because I had this idea that the equation, r2 = x2 + y2, could not be altered. After realizing that I could place the variables in brackets and alter from there, it got much easier.

I didn’t require much help throughout the process, although when needed I did ask my table group. As for techniques, I placed each individual equation out as a model, looking between the picture and the graph to see what I could apply. This worked very well. Overall, this assignment allowed me to better understand how to alter the location and size of a graph relative to the variables placed into the equation, like subtracting or adding from the x, y, or overall value. Not only the size and location, but the distortion as well. It allowed for a better understanding of how manipulating equations really work, as well as assisting with my knowledge of domain and range.

Math Art with Functions! Desmos Project

Link to my project: Ferb

This is a picture of the artwork that I created using functions and relations on Desmos

This is a picture of the artwork that I created using functions and relations on Desmos.

This is the picture that I used for reference to create my project.

This is the picture that I used for reference to create my project.

 

 

 

 

 

 

 

 

 

 

For my Desmos graphing project, I chose to recreate a picture of Ferb, from Phineas and Ferb. I chose to recreate Ferb for a few reasons. First, I loved watching Phineas and Ferb as a kid, and recreating him using functions and relations was quite a nostalgic experience. That being said, I also chose to create Ferb because he is made up of many different types of lines and shapes that I thought would be challenging and enjoyable to try and replicate on Desmos. I feel as though my choice of drawing to recreate was appropriate for the time given and my skill level.

In order to keep my work organized I separated the different parts of my artwork into 5 categories: eyes, ear, head, hair, and clothes. I made the eyes solely using the (x-p)^2+(y-q)^2=r^2 relation . To replicate the ovular shape of the eyes, I multiplied the x value outside of the bracket to make the circles longer vertically.

To make the ear, I used the same relation, but this time I multiplied the y value to make one of the circles wider horizontally. Furthermore, I set the domain and range to cut the ellipses in half. I also used the function y=mx+b to create diagonal lines.

In order to make the shape of the head I used a variety of functions and relations. I used y=mx+b to create the diagonal lines on the back of the head and neck above the ear. I used x=y to the front of the neck and a small portion of the nose, and to create horizontal straight lines for the bottom of the lip as well as part of the nose I used y=x. I used the function y=a(x-p)^3 to create the bottom curve of the nose and the slightly slanted line between the lip and the bottom of the nose. By increasing or decreasing the value of , I could make each parabola wider or narrower. By increasing or decreasing the value of , I could move the parabola horizontally, and changing the value of  would move the parabola vertically. Furthermore, I used y=a(x-p)^2+q and y=-a(x-p)^2+q to create slightly diagonal lines to create the forehead, the top of the nose, and the bottom of the neck. I used the circle relation again to create the top curve of the nose as well as the curve of the lip. I used y=a√(x-p) +q to create the middle of the nose because of the slight curve. Similarly, multiplying x manipulates the width of the parabola, and changing the value of p and q will move the parabola vertically and horizontally

I initially struggled to decide what functions to use to create the hair. I used circle relations to create most of the strands of hair. I also used y=-a(x-p)^2+q to make some of the less curved lines. In some circumstances, two of the curved lines that I used didn’t meet, so I used y=mx+b to create diagonal lines that could connect the two curves. I used y=a√(x-p) +q on one of the strands of hair that didn’t curl under itself. I also used y=sinx to create part of one of the strands of hair. In order to do this, I divided sin by 16 to make the curve longer horizontally.

In order to create the collar of the shirt, I made straight lines by using the function y=mx+b and y=x. I used a circle relation to create the button of the shirt. Lastly, I used y=a(x-p)^3+q and y=a√(x-p) to create the curve of the shoulders.

I also spent some time working with inequalities, but I didn’t include them in my final project because I couldn’t figure out how to create an inequality with an empty circle inside of it (to make the eyes black without filling in the smaller white circle). I also struggled to learn how to make an inequality to go in between two functions without leaving any empty space or going out of the lines. I will continue to research and practice using inequalities in my spare time because I thoroughly enjoyed trying to learn how to use them.

Functions and Relations Used:

  1. x=y and y=x
  2. y=mx+b
  3. y=a(x-p)^2+q
  4. y=a(x-p)^3+q
  5. y=a√(x-p)
  6. y=sinx
  7. (x-p)^2+(y-q)^2=r^2

 

Before completing this project, I had very little experience with using functions and relations, especially on Desmos. As a result, I faced many challenges as I tried to complete this project. When I began working on my project, I didn’t know how to use sliders effectively. As a result, I wasted a lot of time trying to create accurate lines while manually adjusting them. With the help of my peers and Mr. Salisbury, I learned how to use sliders to increase my efficiency. This was definitely an ‘aha’ moment, because I was growing increasingly frustrated trying to plot lines without an accurate ‘starting point’ to work off of. Furthermore, at the beginning of this project, I struggled to remember the impact of each variable on the position and shape of my line. This was quite frustrating as I would accidentally move a line horizontally rather than vertically, ultimately furthering me from the place that I wanted it to be. That being said, through lots of repetition, moving my lines became muscle memory, which increased my efficiency and accuracy.

I feel as though my general ability to estimate the slopes and coordinates that I needed to use improved throughout this project. Initially, it took me a while to orient myself within my picture to choose where to put my lines. Through increased experience and practice, I improved in my ability to accurately guess the general area that I should place my line. Additionally, this project has allowed me to begin easily recognizing the formulas of basic functions and relations. at the beginning of this project I struggled to remember what each function looked like. I had to input each of them into Desmos in order to determine whether or not I should use them. Throughout this project, I gradually began to remember what each function looked like, which allowed me to become more efficient when creating my project. I believe this skill will also help me in future math classes.

Desmos Graphing!

Desmos: Totoro

When it came to figuring out what exactly I was going to draw on a graphing calculator, I had a lot of trouble selecting an image to base my work off of. I considered doing rather complex flowers or characters, but their outlines were so irregularly illustrated that I spent half the class time on the first day searching for the right image. Finally, I just decided to stop looking for something “easy” and do something I actually like. I chose to draw Totoro, a mythical creature in the Ghibli Universe. He had curves and lines, edges and rounded corners, so I thought he’d be appropriate to show my skills in graphing.

In the first few lines I drew, I thought I’d try some guessing and testing, punch some numbers in, and check if it would fit. This method was very ineffective and inefficient, so I looked back on my note package and used some of the things we learned about prior to this project. Sure enough, efficiency went up!

For each of the body parts, I used the following equations and functions.

Hands: Quadratic equations

Nose+Mouth: Circle relation, linear equations

Whiskers: Linear equations

General body outline: Square root function, Reciprocal function, Quadratic equations, Cubic Equations

Feet: Reciprocal equations, linear equations

Eyes: Circle relations

Chest Marks (these took a lot of experimenting to do as they were all slightly different irregular shapes.): Linear equations, Circle relations, Quadratic Equations.

As for strategies, I had a few.

Because Totoro has seven chest marks, all of them slightly different in size and requiring two circles, I copy pasted circle relations in and just changed the variables that needed to be changed rather than plugging in new values to a skeleton equation every single time Totoro needed a circle.

Totoro is also symmetrical in some parts of his body. By copy pasting some equations and by adding a + or – in necessary places, I reflected some lines over the y-axis and saved a lot of time.

I also played around a bit with restrictions as well, using both > and < in them to have fun.

If someone were to ask me what I learned from doing this, I’d tell them I know how to draw things with math now.

That’s a joke –

In all seriousness, I familiarized myself with what different lines from different functions and relations look like. I also got to practice domain and range using restrictions and developed critical thinking every time I thought Hm, that didn’t work. What should I try next? 

Overall, this was a very satisfying project. I have to say, after 80+ equations in desmos, one feels a great sense of accomplishment!

 

Desmos Graphing: Sandy the Squirrel

Desmos Graph

When choosing an image I would be duplicating for the next week using solely functions and relations, I knew that the most logical decision would be cartoon characters for the simplicity of their design. I chose Sandy from Spongebob predominately because of the curves of the drawing, which I thought would be easy to replicate using circles and parabolas. However, this wasn’t the case when I recreated the drawing. I ended up using a variety of parabolas, quadratics, circles, linear equations and even an exponential function. Lines I thought would simply use circles I ended up using a multitude of parabolas and quadratics on. Before I applied any equations to the graph, I looked at my initial picture and imagined what lines would work best to replicate that shape. I used that strategy throughout the project, deviating when things didn’t look quite right and using the next probable equation to remedy the problem.

The only real struggles I faced were the transformations of the lines. I figured out early on that by making the x and y variables negative I could perform vertical and horizontal reflections of equations over the axes. Occasionally I would need to perform angular rotations or in one specific case, an overall increase in the size of a sin function, and would have no idea how to do so. To resolve this, I looked for alternative ways to carry out the task. This may have resulted in more work to achieve the same result, but I worked with what I knew. This project helped me develop and apply my knowledge of relations and functions while thinking of them more visually and less like simple numbers and letters on a page.

Math Graphing Art Project

R34 Graph link

I decided to make an R34 GTR on Desmos Graphic Calculator. I used linear, quadratic, cubic, square root and circle equations to fulfill my mission.

Guide:

Black line: linear function

Green line: straight linear function

Blue line: quadratic function

Red line: cubic function

Orange line: square root function

Purple line: circle equation

I was surprised to find how many of the car’s lines perfectly fit different functions. Luckily, this car is quite boxy, which made it easy for me to style the complicated front with linear functions. For the linear functions, I only had to make slope changes, vertical translations and domain limits. The lines on the hood of the car reminded me of square root function graphs, so I adjusted square root functions using expansion/compression, horizontal translation, and vertical translation to fit those lines. Quadratic functions came in handy for long horizontal curves, like the horizontal lines of the front splitter and roof. To tailor a quadratic function to a line on the car, I would use horizontal translations and vertical translations, domain limits and expand the parabola to a very shallow curve. In some cases, I would also make the quadratic equation negative to make a downwards curve. I used a cubic function once, on the rear of the car. It fit perfectly with the curve of the line between the rear bumper and the roof. I used horizontal and vertical translations to fit it in the right place, domain limits to make the line the correct length and expanded the hyperbole to fit the curve. Circle equations were very handy when making the wheels and vertical curves on the doors. I used horizontal and vertical translations to get the circle in the right place, and then adjusted the other variables to make the ellipse shape in wanted. Afterwards, I would set domains and ranges to have only parts of the circle there. In some cases, I would have to use two circle equations in the same place with different domains and ranges to get the desired parts of the circle or ellipse. By the end of the project, I felt like I knew exactly what each variable did in each equation and could correctly estimate correct variables for a function to make the graph I wanted.