Intro to Quadratics
Over these last couple of weeks, Class D been overlooking quadratics in math . This has been a challenging few weeks, because it was combining my two worst enemies: kinematics and quadratics. In quadratics, we learned vertex form , standard form, and factored form. The objectives over the course was to understand and be able to identify what parabolas are and how they work. We completed around twenty four worksheets that were handed in and graded by Dr. Drew.
In the beginning, we were introduced to kinematics. Kinematics works with the motion of objects with reference to the forces that cause the motion of objects(physics). Usually it ties in with the math of flying stuff, such as airplanes, or rockets, because of the curvature in the flight pattern from take off to landing. We launched our quadratics project with the, "A Victory Celebration" handout. This paper dealt with the kinematics and physics of a firework being launched off a tower to celebrate the High Tech High sports team.
In the beginning, we were introduced to kinematics. Kinematics works with the motion of objects with reference to the forces that cause the motion of objects(physics). Usually it ties in with the math of flying stuff, such as airplanes, or rockets, because of the curvature in the flight pattern from take off to landing. We launched our quadratics project with the, "A Victory Celebration" handout. This paper dealt with the kinematics and physics of a firework being launched off a tower to celebrate the High Tech High sports team.
Vertex Form
We started this project looking at parabolas, and we learned that one way a parabolas equation can be expressed is in vertex form. This was the first form of many of the many other quadratic equations that we started learning in this block. This is the vertex form: y = a(x-h)2+k. To better understand how a, h and k in this form affect the location, depth, and width of the parabola we used multiple handouts and online graphic calculator called Desmos. The first equation that is used in the part one of the Parabolas and Equations packet is y+ax^2. This equation was used to understand how a affects the width of the parabola. With the graphing calculator I was able to understand that a larger a makes the parabola smaller, and a parabola is larger if it has a smaller a. There was also an effect on how the parabola took shape on the graph. If it is a positive a then then the parabola is concave up, but if it is a negative a then the parabola is concave down. For part two of the Parabolas and Equations packet we learned how k affects the highest and lowest part of the parabola. We also learned that the Y coordinate is equal to k because of it’s positioning on the vertex. For part three, the final part we learned about h is similar to k in a sense that it controls the X coordinate on the vertex.
We moved onto a new paper, Vertex form for Parabola to compile all of the information that we had learned from the three papers that we had just went over. I have to say that this is where I started to get confused by the work that we were doing so I looked to my partners for help. It was explained to me that we were using the knowledge we now have of a,h and k to finding the equation of a parabola. This information we could now use to find the vertex in the rocket problem. This was a moment where all the stress and confusion that a lot of us went through started to make sense. I feel like I am not the type of learner that needs to be put through loops for me to understand what the problem is asking, and I wish that these problems were given to us prior to starting the project.
We moved onto a new paper, Vertex form for Parabola to compile all of the information that we had learned from the three papers that we had just went over. I have to say that this is where I started to get confused by the work that we were doing so I looked to my partners for help. It was explained to me that we were using the knowledge we now have of a,h and k to finding the equation of a parabola. This information we could now use to find the vertex in the rocket problem. This was a moment where all the stress and confusion that a lot of us went through started to make sense. I feel like I am not the type of learner that needs to be put through loops for me to understand what the problem is asking, and I wish that these problems were given to us prior to starting the project.
Various Forms
(Graph #1)The standard form of a quadratic equation is ax^2+bx+c=y. This is the form gives us the y intercept through the value of c. It is much more simple then the other forms, causing it to be used more widely.(Graph #2) The factored form of a quadratic equation is (x-p)(x-q)=y. This is the form gives us the x intercept.
Converting
Solving Problems
Kinematics (projectile motion): As a volleyball player I can use Kinematics to understand if the time that the volleyball stay in the air is shortened, then the reaction time for my opponents is shortened. Kinematics is also useful for when I am trying to determine the trajectory of the ball which helps me better my accuracy for games and practice. Geometry (triangle problems and rectangle area problems): I now have the understanding of how to create symmetrical shapes for when I work on future projects in class. I have the understands of how to measure triangles and find the area of a rectangle. Economics (maximizing revenue/profit or minimizing expenses/losses): As I continue to grow and become part of this world, I will have a better understand of how to control revenues and expenses. I can use this in my everyday life. If I am interested in becoming a manager of profit, I will have this knowledge in my back pocket.
Reflection
This was not one of the blocks that I was really passionate about understanding, however I really applied and pushed myself to accel. It was a rocky start, considering I was getting very distracted by other people who were also not very interested in learning. I would leach onto other people to get the answers last minute and I remember the exact moment when that all stopped. I had just handed in a packet that was half done and not up to an a level and my teacher said to the class that you can always copy off of someone's work, but you will never be able to explain to me what we are learning in class. You can get an A, but you will struggle for the rest of your school year. This really hit me considering it was something I already understood, but never took the time to really consider. I decided from that point on I was going to start working on my own and push myself to ask questions and get help from people who were willing. I asked my table mates, my dad, and almost anyone I could to help me. I'm still not very happy with my standing in math class, but I know I am working my hardest and I will get to where I need to be. I worked hard to complete my assignments, yes there were times when I slipped up and didn’t give myself the time to finish an assignment, but I tried my hardest to complete everything that I needed.
Habits of a Mathematician
Look for Patterns:
One area that where I looked for patterns was when we first began to use graph to understand how a,h and k affected the parabola. It was very important to observe in the changes I made and the ones that spawned.
Start Small:
When I worked with my partners and we came across problem that was challenging we would start small and work our way to open up the problem. There were times when it was wrong, but we learn from our mistakes.
Be Systematic:
When we started to work with converted one form to another, it was important to be systematic with each of the operations.
Take Apart and Put Back Together:
When we we're working with completing the square we had to take apart the equation to add what we needed.
Conjecture and Test:
There was multiple moments when my partners and I would test something to see if there was any credibility and come up short. Once we did our own testing we would ask our teachers for help, knowing that we didn’t know how to do it.
Stay Organized:
Organization was a big part of this block, but I only made a big deal out of half way through. I lacked in this habit, but I can now understand how important it is in math.
Describe and Articulate:
When my partners and I would mess up we would have to explain to our teacher how we got to that point of confusion to return ourselves back to understanding.
Seek Why and Prove:
Every part of this block was followed by why it was and how we can prove it to ourselves. I feel that because I had this requirement apart of the project, I have a better understanding and ability to explain it.
Be Confident, Patient and Persistent:
I am not the type of person to ask teachers questions, but I decided that to grow and learn in this block I needed to take it upon myself to ask as many questions as possible.
Collaborate and Listen (with Modesty):
I worked with a big part of my classmates and learned that I work well with a lot of people that I never thought I would because of this project.
Generalize:
Throughout this whole block I was looking back at my note, because I generalized everything that we learned to help me understand the next steps.
One area that where I looked for patterns was when we first began to use graph to understand how a,h and k affected the parabola. It was very important to observe in the changes I made and the ones that spawned.
Start Small:
When I worked with my partners and we came across problem that was challenging we would start small and work our way to open up the problem. There were times when it was wrong, but we learn from our mistakes.
Be Systematic:
When we started to work with converted one form to another, it was important to be systematic with each of the operations.
Take Apart and Put Back Together:
When we we're working with completing the square we had to take apart the equation to add what we needed.
Conjecture and Test:
There was multiple moments when my partners and I would test something to see if there was any credibility and come up short. Once we did our own testing we would ask our teachers for help, knowing that we didn’t know how to do it.
Stay Organized:
Organization was a big part of this block, but I only made a big deal out of half way through. I lacked in this habit, but I can now understand how important it is in math.
Describe and Articulate:
When my partners and I would mess up we would have to explain to our teacher how we got to that point of confusion to return ourselves back to understanding.
Seek Why and Prove:
Every part of this block was followed by why it was and how we can prove it to ourselves. I feel that because I had this requirement apart of the project, I have a better understanding and ability to explain it.
Be Confident, Patient and Persistent:
I am not the type of person to ask teachers questions, but I decided that to grow and learn in this block I needed to take it upon myself to ask as many questions as possible.
Collaborate and Listen (with Modesty):
I worked with a big part of my classmates and learned that I work well with a lot of people that I never thought I would because of this project.
Generalize:
Throughout this whole block I was looking back at my note, because I generalized everything that we learned to help me understand the next steps.