Written Response

My quadratic function is very different compared to its parent function. This is shown through its many added variables, this includes the a, h, and k which all represent different transformations and parts of the graph. Seen in my graph, the vertex of my parabola is (-6,-5) this not only represents the h (-6), but also represents the k, which is equal to -5. The h represents multiple things in the graph, it represents not only the amount the parabola is shifted left or right, but also the axis of symmetry. Evident within my graph, as the h is equal to -6, the graph is shifted left 6 units, and also the axis of symmetry is x = -6. Similar to h, the k represents multiple parts of the graph; this includes the range, min/max value, and how much it is shifted up or down the y-axis. Seen in my graph, as the k is equal to -5, not only is the range less than or equal to -5, but also the minimum value is also -5. Therefore, the whole parabola is also shifted down 5 units. Lastly, the a may be one of the most influential variables of the vertex form, not only does it show if the parabola is stretched or compressed, it also displays whether the parabola is opening down or up. This can be determined through looking at the value of a to evaluate whether a is larger than 1, or a fraction between 1 and 0 and whether it’s negative or not. For example, as my a was equal to -2, it represents that my graph will have a more compressed parabola opening towards the negative quadrants.

Self Evaluation

1. I represented the fundamental mathematical ideas in multiple ways through representing the differences that h, k, and a represent within an equation.
2. Evident within my paragraph, I have demonstrated a sophisticated amount of mathematical vocabulary. This is shown through the use of terminology as vertex, axis of symmetry, and an extended amount of vocabulary first presented to students.
3. Not only did I include all necessary information about my parabolas on my graph, I also presented the information in my paragraph in a clear concise manner, addressing all appropriate information one by one.