Communicating & Representing Assignment:
Blue: My Parabola y= -1/2(x+7)^2 – 4, Red: Original y=x^2
The equation of my parabola in this assignment y= -1/2(x+7)^2 – 4 can be compared and contrasted to the original parabola’s equation of y=x^2 in a network of ways. The image above represents how my parabola is seen in context to a graph as well as how it may contrast visually to a standard parabola equation.
Variables A, H, and K are the variables represented in our equation y=a(x-h)^2 + k, and they are primarily what differentiates the two shown parabolas and what makes them significantly different. In this case, the A is -1/2 and the A is responsible for the width of a parabola and in my example my parabola equation is shown to be wider than the original as it is shifted -0.5 units vertically opposed to 0. Since there is a negative in front of 1/2 it also flips the parabola below 0, making it fall in the downward direction. In addition, my H value which is +7 along the x-axis, is responsible for creating a horizontal shift within my parabola whereas the original is only 0 along the x-axis. In my equation, the +7 resulted in a shift of 7 spaces to the left as the positive sign correlates to the opposite, in this case, a horizontal shift of -7. Finally, the K results in a difference in the vertical shift of the parabola; in this specific instance, my parabola has a shift of -4, whereas the original parabola has a shift of 0. As a result of these shifts, the vertex changes from (0,0) to (-7,-4).
Self Assessment
1. Give an example from this assignment where you represented the same mathematical idea in three different ways? (for example, as a graph, an equation, and in words)
I was able to represent three different mathematical ideas by communicating my overall understanding of the 3 main principles which were the values A, H, and K. These principles were represented through the desmos graph as it showed visual differences between the original equation compared to mine. In addition, it was also represented through my equation as from a visual and critical standpoint it was quite easy to tell that my equation would not result in the same parabola as the original. Finally, I was able to inflict these principles in my paragraph by providing examples of why my graphs features are shown as they are as well as why there is a drastic difference in the two parabolas based upon the three main principles A, H, and K.
2. Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.
My mathematical vocabulary was represented throughout my explanation by using terms such as vertical and horizontal shift, implementing key parts of a parabola like a vertex and expanding upon it, as well as using appropriate, sensible, and clear language to give the reader a persistent flow.
3. Give an example from this assignment where you used formatting to share the information in a clear and organized way.
By using proper terms, efficient sentence flow, and distinctive separation between different ideas/questions, I was able to elaborate and share information in a clear, structured, and efficient manner. Overall, this improved the flow of the assignment and made it easier to locate any errors I may have made in addition to producing an excellent presentation.