​Problem Statement

Over the course of these two weeks, we've been working with desmos to get introduced to parabolas and testing out different equations that would make them be up, down, left, right, upside down, slimmer, and wider. We did 5 activities in total, each was different from each other and challenged us.

Process and Solution

Will it Hit the Hoop?

This is the first activity that we did. We used parabolas to guess if the guy would make the basketball into the hoop or not. Most of my answers were very short and I didn't go much into detail about my predictions. I guessed that this shot would go in because of the arch and the line shows that the ball is going to go through the hoop. From this activity, I was introduced to parabolas and how they can be used in various ways.

Polygraph 1 (Guess Who with Parabolas)

This is the second activity we did. It's like "guess who" except the parabolas are the people. My partner asked very good questions that were able to eliminate a lot of parabolas. As you can see, my partner started to ask questions that included the vocabulary that we had learned. Such as, "Is your parabola concave down?"

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Polygraph 2

This is the third activity that we had did. From this activity, we learned new vocabulary such as concave down, concave up, vertex, etc. We also learned how to sketch parabolas at certain points. As you can see, I sketched a parabola that's concave down with it's vertex at (4,-2). Once we learned the vocabulary, we kept on using them to become more familiar with their meanings. Some new vocabulary we learned were:

• Concave Up - Looks like a smile
• Concave Down - Looks like a frown
• Vertex - Turning point

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Match My Parabola

This is the fourth activity that we did. This is the activity that we spent the most time on to deepen our understanding on how we can create parabolas that pass through certain points. In order to make some parabolas concave down, I had to add a negative sign at the beginning of the equation. In order to make the parabolas wider, I learned that I had to use a decimal because whole numbers would just make the parabolas slimmer. The smaller the number, the wider and the bigger the number, the slimmer.

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Marble Slides

This is the fifth and final activity that we did. For this activity, we had to create parabolas for the marbles so that they were able to collect all the stars. As you can see, it says. "Success!" because I was able to make a parabola that helped the marbles collect the stars. This activity was the most challenging one for me because I first had to start of with plugging in random numbers in order to get somewhere. As soon as I was able to create multiple parabolas, I eventually got the hang of it and learned how to manipulate them in various ways.

Problem Evaluation

Working with desmos was very new to me since I had never worked with it before. Even though desmos was new to me, it was nice to learn about parabolas in a fun and educating way. I do wish that we were able to have more time on the activities, because sometimes I would have to stop during the middle of an equation, and then when we worked on it the next day, I wouldn't remember where I had left off.

​Self-Assessment

I do admit, at times I would slack off and joke around with my table mates, but I did try my best when trying to create parabolas. I would sometimes get stuck, and not know where to start which resulted in me asking my table mates for help and seeing what they had tried. My goals for this semester were to have more confidence in math and ask questions when something is confusing for me, so I tried my best to do just that. When my table mates found a solution, and I didn't, I would ask them how they got that and they would give me suggestions on how to get started. I believe that I deserve an "A" because I did put effort into finding equations even when I was feeling stuck and discouraged.

​Things I Learned

When working with desmos, I learned multiple things such as what vertex form is, how to make a parabola wider, how to apply restrictions, etc.

• Vertex Form is very powerful at helping you transform a graph. When creating parabolas on desmos, we kept on writing equations in that form. (y=a(x+h)^2+k​)

​a - how slim or thick the parabola is going to be and also determines if the parabola is going to be concave up or concave down
(y=(.15)(x+h)^2+k)
h - the amount of spaces the parabola is moving left/right
(y=a(x-h)^2+k OR y=a(x+h)^2+k)
k - the amount of spaces the parabola is moving up/down
(y=a(x+h)^2+k OR y=a(x+h)^2-k​)

• Decimals play an important part when creating parabolas. When you add a decimal at the beginning of an equation, it determines how wide a parabola is going to be. The smaller the decimal the wider the parabola is going to be.
• Asking questions with appropriate terminology was something that I learned. When Kirby and Anatole showed us the new vocabulary, they encouraged us to use them when we worked on all the activities. They emphasized that we use the vocabulary when playing "Guess Who" with parabolas so that we were familiar with the words and their meanings.

​Edits

Luz suggested that I add the number of each activity so it looked more structured. So, I decided to just add the title instead so that it would be more clear on what activity the viewers are looking at.