![](https://mycentennial.sd43.bc.ca/zahraa2021/files/2024/04/desmos-graph-1-64a2f2968d3a3b6e-1024x1024.png)
![](https://mycentennial.sd43.bc.ca/zahraa2021/files/2024/04/image-33f6cdadfb2dd0d2.png)
The significance of a, h and k in my equations————————————————————–
A parabola that has been shifted to the right of the parent function:
![](https://mycentennial.sd43.bc.ca/zahraa2021/files/2024/04/image-c86dbe9e13850ad6.png)
- If the value of a is less than 1 then it is wider. Since a = -1, the parabola opens downwards and it is wide.
- In this equation, h=8, which means the vertex of the parabola is shifted 8 units to the right along the x-axis. If h>0, the shift is to the right, and if h<0, it’s to the left.
- Here, k=8, so the vertex is shifted 8 units upward along the y-axis. If k is positive, the shift is upward, and if k is negative, it’s downward.
A parabola that has been shifted lower than the parent function:
![](https://mycentennial.sd43.bc.ca/zahraa2021/files/2024/04/image-b359516d56c21f2c.png)
In this equation we have no horizontal shift, our vertical component is -5 along the y-axis. Our ‘a’ is smaller than 1 therefore we have a wider positive parabola.
A parabola that opens down and is more narrow than the parent function:
![](https://mycentennial.sd43.bc.ca/zahraa2021/files/2024/04/image-25c754d9c85575f8.png)
In this equation we have no horizontal shift along with no vertical shift. Our ‘a’ is negative and more than 1 means that this parabola is narrow and opens downwards.
A parabola that opens up and is wider than the parent function:
![](https://mycentennial.sd43.bc.ca/zahraa2021/files/2024/04/image-fd966d7061b333d9.png)
In this equation we have no horizontal or vertical shift again. However our parabola opens up and is the widest one we have since it is the smallest ‘a.’
![](https://mycentennial.sd43.bc.ca/zahraa2021/files/2024/04/image-c8214e63f1e7b158.png)
This is the parent function.
Self-Assessment————————————————————————————————
How did you represent the same mathematical idea in multiple ways in this assignment?
I represented the same mathematical idea in multiple ways by equations, graphs, coloring system and explanations. One of them being functions in vertex form y = a(x – h)^2 + k. And in y = ax² This demonstrates an understanding of functions, showcasing how they can be represented in different forms while conveying the same mathematical concept.
I came up with five distinct quadratic equations, ensuring that each met the specified requirement. In order to enhance the clarity while graphing these equations on Desmos, I applied a color coding system to visually distinguish each function enhancing the clarity. This served as a form of mathematical communication, effectively linking the graphical representation with its corresponding equation (which included the vertex as well.) Therefore, I’m representing the same mathematical concept, presenting it visually through graphs and symbolically through equations, with color acting as the connection between the two representations.
Furthermore, by graphing both forms of the function, I visually confirmed their corresponding shapes and transformations. This hands on approach solidified my comprehension of how changing parameters such as ‘a’ can shift and reshape the parabola on a graph.
By graphical representations with mathematical analysis, I demonstrated a comprehensive understanding of transforming parabolas and showed the same mathematical idea through multiple representations.