Transforming Parabolas

Equations:

  • The quadratic parent function : y=x^2, red graph , vertex : (0,0)
  • A parabola that opens up and is wider than the parent function: y=3/12(x+6)^2+2 , purple graph , vertex :(-6,2)
  • A parabola that opens down and is more narrow than the parent function: y=-2x^2-2 , green graph , vertex: (0,-2)
  • A parabola that has been shifted to the right of the parent function: y= 3(x-2)^+2 , blue graph, vertex:(2,2)
  • A parabola that has been shifted down lower than the parent function: y= -x^2-9 , orange graph , vertex : (0,-9)

In our equations, the letters “a”, “h”, and “k” have an enormous impact on our parabolas. In our purple parabola, the letters “k” and “a” effected the shape of it as well as our direction. our purple graph is wider than our parent function, because our “a” value is 0<a<1 which caused our parabolas appear wider than our parent function and make the parabola U-shaped and has been opened upward . The “k” letter made our parabola be above our x-axis by being positive. If our “k” value was negative, our parabola would be shifted under our x-axis and our parent function. The green parabola has been opened downward and more narrow than the parent function , as well as opened above our x-axis, due to our “a” and “k” values. The “k” value is negative so our graph is under the x-axis and our parent function. Our “a” value is also negative which made our parabola open downward , and the more narrow shape than our parent function, because the value is a<-1. The blue parabola has been shifted to the right if the parent function due to the effect of the letter “h”. In the blue parabola h=+2 , so our parabola shifted two unites to the right of the parent function. The orange parabola has been shifted down lower than the parent function due to our “a” and “k” value, which are negative. “a” value made the parabola opening downward, and the “k” value shifted the parabola down, under the parent function.

  1. How did you represent the same mathematical idea in multiple ways in this assignment? I used the same mathematical idea in multiple ways by understanding the definition of the vocabularies used in the chapter, as well as understanding the function and the effect of different letters( “a” , “k” , “h” ) on the parabolas and the equations.
  2. State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.

The vocabulary words that I used include “y” and “x” intercepts , axis of symmetry, vertex, domain, and range

  1. How did you use formatting to share your information in a clear and organized way? I used graphs, equations, and vocabulary words to write my responses for formatting my Information in a clear and organized way.

Reviewing Chapter 1: Factoring & Radicals

The part of chapter 1 that I am most confidant, and comfortable is factoring, solve by factoring, simplifying radical expression, Identifying restrictions, knowing the meaning behind each words, and the concept behind them. This comfort is due to the mistakes that i made during group works, completing all the assigned problems, and making clarification through questions.

The part of chapter 1 that is difficult for me is rationalizing the denominators, and finding common index. These parts are the most challenging parts for me due to the less practice, as well as not being able to understands the concept before each problem. I will try my best to improve by spending more time to practice, and ask for help if i need till the end of the course.

I usually learn new material best when I like the method that the teacher use for each part of the course, and enjoy being in the class. As someone who is shy, I sometimes struggle to ask questions out loud, so i find private explanations more effectively. I enjoy challenging questions because they make me to think more, as well as memorize their formulas better. Most of my learnings are from practicing with different questions, and read the notes before the lesson.

I plan to prepare for the unit test by completing all workbook questions , the extra practice on teams, and redoing handouts. I have already completed all assigned handouts, so the only things that i need to get done are some of the workbook questions that are left, and the extra practice sheets. I plan to be finished by Wednesday’s morning.

I have already completed all the assigned practice problems, and redone them for the test.

“I persevere with challenging tasks and take ownership of my goals, learning and behavior.” This statement can have different meanings for each person. personally, this statement for me is the challenge that I am taking ,and facing this semester. Also, for me, this is the statement of math class. Math is full of challenges and tricks. it also needs a lot of patient and focus, and they are all connected to what your goal is. Math teaches valuable lessons in focus, patient , and problem solving, that helps everyone to achieve both of their academic, and life goals.

Iran-Core Competency Reflection

when i was working on this work of art, first i felt frustrated, it was my first time working on something like this so i had a lot of stress to see how it is going to turn out when i am done with this work. i am kind of proud of how it turns out because i was not that bad. It helped me a lot with my other works and now i know how to use each element for the art that i am working on.

INS Presentation Self-Reflection

In my opinion, my presentation did not go very well. I thought I was ready for it, but when I started talking, I realized that I wasn’t ready for it at all and it didn’t go the way I had in my mind. But I tried my best to keep my composure and be able to express the words well and think that I was successful .Next time I will make sure that I know everything and take notes so that I don’t forget anything. This was my second experience in the presentation and I am sure that I will be better next time with this experience.


Journal

Reflection

I really like writing a journal , this whole time I tried my best to write a lot of journals. I even write a journal for myself sometimes. Writing journal every week helped me a lot and made me more interested in writing. In this way I can find my mistakes in writing and fix them. Every week we learned something new about journaling . I tried to write my own journal that day according to the things I learned so I don’t forget them. In the end , I can write my own journal now . I know that I still have some mistakes, but its much better that before and I am proud of myself in writing.

Stock Market : Self Assessment

What is the difference between a stock and a bond?

The difference between a stock market and a bond is that stocks give you partial ownership in a corporation , but the bond are a loan from a company or government.

How are risk and return connected?

risk and return are related . The greater the risk that an investment may lose money , the greater its providing a return. Therefore , the smaller the risk an investment poses , the smaller the potential return it will provide.

What does it mean to have a “well balanced portfolio?”

Typically , balanced portfolios are divided between stocks and bonds , either equally or with a slight tilt , such as 60% in stock and 40% in bonds.

How much information did you use to help you with your decision-making process?

i used the information that i got in the class and also by searching about the question at google

Has investing become a more approachable or attainable concept to you?

After these information , yes it become more approachable for me because i did not have any idea about it , but now i know a lot about it so its easy and attainable if you work hard for it.

What is something that you have learned which you have changed your mind about?

I thought that its really hard and it was not something that i was look forward it but now , i really want to know about it and get more information and search more to maybe start learning from know .