Pre-Cal 11 Parabola

Equation

y=x2 is the parent function while 𝑦=βˆ’1/2(π‘₯βˆ’3)2 βˆ’4 is my given function.

Graph

Each line is colour-matched to the equations above, the red line is 𝑦=βˆ’1/2(π‘₯βˆ’3)2 βˆ’4, while the purple line is the parent function y=x2.

Significance of a, h, an k in “y=a(x-h)2+k”

  • “a” in my function is -1/2, the significance of it in my function is that it determines the width of the function. Since there is no “a” in the parent function it assumes its 1, so that for every “y” it equals x times itself. The width of the parabola is affected by β€œa”, as if the number is bigger the parabola is narrower, and if it’s smaller (like a fraction) it becomes wider as β€œa” gets closer to 0, if β€œa” is a positive number it will open upward with a minimum value and if it’s a negative number it will open downward with a maximum value.
  • “h” in my function is 3 (because the original equation being (x-h)), h determines where the vertex of the function is on the x axis, as shown in the graph above the red line being my function is shifted over to positive 3 on the x axis (x=3). The parent function is on x=0 because theres no “h”, so it assumes it’s 0 since no number is given.
  • “k” in my function is -4 and the significance of this number is that it determines the vertex on the y axis, in my function the line is shifted y=-4 down alongside x=3 from “h” above. Similar to “h” if theres no number representing “k” it’s just assumed to be 0 therefore the parent function is laying on (0,0) because of this.

Self-Assessment

  • Q – Give an example from this assignment where you represented the same mathematical idea in multiple ways.
  • A – I explained how “h” and “k” are similar in their rules on how it affects the vertex on both the x and y axis respectively, I stated that they share the rules that if there’s no number representing them it’s assumed to be 0 given the parent function.
  • Q – Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.
  • A – I used terms like “function”, “vertex”, and “axis” to demonstrate my math vocab and also explain in the case of vertex what it does, it moves the point of the line on the x and y axis.
  • Q – Give an example from this assignment where you used formatting to share the information in a clear and organized way.
  • A – I used tools given from the blog editor such as headers and image embedding. I also presented my information in chronological order in relation to the requirements on teams. Lastly I used bullet points to separate the “a”, “h”, and “k” significances from each other as well as giving context to the screenshots above.

Favorite Recipe

Fried Rice

Making and Sharing Reflection

Making this recipe had crucial steps to make the outcome of this, some of the steps is to cook the rice ahead of time so this recipe can be fast when we make it with all ingredients ready. Another is to perfectly cook the egg so it doesn’t overcook in the fried rice. Chopping and preparing the ingredients is key so the fried rice has small bite sized veggies. Cooking the veggies to perfection so that they don’t overcook is also crucial. Lastly the sauce is the 2nd important ingredient to this dish as it provides the fried rice taste.

Core Competency Reflection

The 4 Core competency’s I chose were:

One of the ways I ensure my group is clear on the common purpose is to… – check with them and review what each of our jobs are ahead of cooking.

I know the group is working well together when I hear/ see… – Good communication, no arguments, and some fun as well.

If the group is not productive, we can …. in order to get things moving in the right direction. – we can work together to solve our problems.

As an active listener, I notice that I … – If anything is changed on the recipe, if there are key steps, and if there’s techniques to use.

One goal I have is to work with people and take bigger roles when needed and the ways I communicate. Ways to achieve that is to be prepared and have a good attitude.

Favorite Recipe

Scones and Apple compote

Making and Sharing Reflection

I am reflecting on “Create food products, working individually or collaboratively, and making changes as needed” and “Critically evaluate the success of meals, and explain how design ideas contribute to the individual, family, community, and environment. I think I had done good in creating food products and working with others or by myself as the more recipes we did. After a couple of food labs I got the hang of working in groups of 3, in partners, and by myself when my partner is going for ingredients or if I am going for ingredients. I also did make changes in the event it was needed such as if my partner was away for one of the labs, I was able to adjust. The only struggle I had was a bit of communication while in the process of cooking. But I overall think I did great. I also properly evaluated the meals I created, if they were good or not, and if I would ever make them again.

Core Competency Reflection

Here are my 3 core competencies:

  1. As an active listener, I notice that… : I chose this core competency because I noticed that when I actively listen I can learn some important things that help me later on. I also notice when I actively listen I could help improve my grades in some way.
  2. I know when the group is working well together when I hear/see : I chose this because the group had properly made the scones and were properly communicating.
  3. If the group is not productive, we can … in order to get things moving in the right direction : I chose this because when we didn’t work productively, I would always try to help and solve the issue to keep working.

One goal I have going forward is being better at showing how I value feedback, I think sometimes I take feedback a bit too personal and it could lead to a bad group experience, so I want to improve in that.