Tag Archives: CommunicationCC

Transforming Parabolas

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y = x²

y = 6(x+4)² – 5

y = -3/2(x – 3)² + 1

y = 1/6(x – 7)² + 1

y = 1/65x² – 10

In each of these equations, the parameters a, h, and k play crucial roles in determining the transformations of the parabola y = x². The value of “a” controls the vertical stretch or compression and the direction of the parabola. When “a” is greater than 1, as in y = 6(x+4)² − 5, the parabola is vertically stretched, making it narrower than y=x². In contrast, when “a” is between 0 and 1, as seen in y = 1/6(x−7)² + 1, the parabolas are vertically compressed, appearing wider; this transformation is made more dramatic in y = 1/65x² – 10. If “a” is negative, as in y = −3/2(x−3)² + 1, the parabola opens downward, indicating a reflection across the x-axis. The values of “h” and “k” independently control the horizontal and vertical translations. The “h” value moves the parabola left or right; for example, in y = 6(x+4)²− 5, shifting the parabola 4 units left. The “k” value, like in y = −3/2(x−3)² + 1, where k = 1, moves the parabola vertically, in this case, 1 unit up. By examining the graphs of each equation, I could see how each transformation affected the width, direction, and position of each specific parabola, with the differences in stretch, compression, and translations visible between the graphs.

Self-Assessment

How did you represent the same mathematical idea in multiple ways in this assignment?
I represented the transformations of parabolas by using equations and corresponding graphs. The equations showed how changes in “a”, “h”, and “k” values transformed the shape and position of the parabolas, and the graphs provided a visual representation of these transformations.

State some of the relevant mathematical vocabulary words you used to demonstrate your understanding and their definitions. State where you found the definitions (your own memory, class notes, online?).
I used terms like “vertical stretch,” “compression,” “reflection,” “horizontal translation,” and “vertical translation.” These terms came from my memory and class notes, where we discussed how each part of the parabola equation affects the graph.

How did you use formatting to share your information in a clear and organized way?
I used a paragraph format with logical progression, introducing each parameter (a, h, and k) and explaining its effect on the graph. In addition, bullet points for the self-assessment kept my responses organized and easy to follow.


Spanish 10 Core Competency Reflection

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Creative Thinking

Reflecting on the creative writing core competency through my experience with Paxton on the Spanish script, I realized the importance of collaboration and imagination. Working together, we enhanced our creativity by sharing ideas with each other. Our dialogues expressed the storyline and showed our characters’ emotions. For example, when our team was losing, Paxton’s character stayed positive. After winning the championship, we brainstormed activities like a picnic or a trip to the beach, basing our ideas on the weather. When our characters heard a mysterious thump while driving in the car, we quickly came up with a plan, introducing an unexpected twist. This experience helped me appreciate how creative writing involves creating interesting plots and dialogues, collaborating effectively, and quickly thinking.

The script I made with Paxton shows how we work together and come up with cool ideas, which is what creative writing is about. We learned to adjust our plans quickly when things changed, like when we had to change our story because of the weather. I got better at making characters with different feelings, but I want to get even better at making our stories more surprising and exciting. Just like writing a short English paragraph, making this script needed us to talk and work together to make a fun story.

  1. I can work with others to create interesting stories. Working with a partner helps me think of new ideas. Together, we make our stories more exciting and detailed.
  2. I can come up with new ideas and adapt to changes. When plans change, I can think quickly and adjust. This makes our stories flexible and creative.
  3. I can develop characters that show different emotions. I create characters who feel and react in realistic ways. This makes our stories more engaging and relatable.