My assigned parabola has been transformed horizontally, vertically, and has also been reflected to open downwards from the original parent function.

The formula for a parabola is y=a(x-h)²+k.

The coefficient a is responsible for changing the width of the parabola. If a is greater than 1, it will cause the parabola to compress or become more narrow, but if a is 1>a>0 or 0>a>-1, it will cause the parabola to stretch or become wider. The coefficient a will also cause the parabola to open downwards if it is negative.

In my assigned parabola, the coefficient a is -¼, which is between 0 and -1. This results in the parabola being stretched and becoming wider than the parent function. It is also negative, which causes the parabola to open downwards.

The variable h is responsible horizontal transformations. In the assigned parabola, h = -1, which results in the parabola being shifted to the left by one from the original parent function.

The variable k is responsible for vertical transformations. In the assigned parabola, k = -4, resulting in the parabola being shifted downwards by four units from the original parent function.

H and k also tell us where the vertex is, or where the parabola begins to open. The vertex of the assigned parabola is (-1,-4).

Core Competencies

I utilized multiple methods of explaining the same mathematical idea through my use of graphs, the quadratic function itself and written explanation. To explain my quadratic function, I used a picture of the function itself, but also included a photo of the function on a graph. I also explained the different variables in the function to make it understandable.

I showed my understanding through the mathematical vocabulary I used to explain what each variable represented. For example, when explaining the significance of the variable h, I used mathematical vocabulary such as horizontal transformation to explain the parabola being moved to the left as a result of the value of h being -1.

In the assignment, I formatted it so that there was a separate paragraph for each variable that I was explaining, making the entire post easier to read and understand in comparison to a post where all of the text was in one paragraph.