Desmos Graph of Equation and Parent Function

Significance of a, h, and k Within the Equation

In my equation, a was represented as ½. Due to the fact that the coefficient on the x² value (a) is a positive number the parabola created by my equation opened upwards rather than downwards which is what would’ve occurred had the coefficient been a negative number instead. The coefficient of the equation also determines what the parabola will look like in terms of width, shape and direction. The coefficient of my equation is ½, and because the coefficient is in between 0 and 1 it means that my parabola will be wider, which can be seen on the graph, rather than compressed had the coefficient been greater than 1. The value of h in the equation I was given is 6, it is a positive number due to the fact that when it is plugged into the equation y = a(x – h)² – k, the 6 becomes a negative number. This means that the parabola’s vertex will be shifted 6 spots to the right of the parent function which in this case is 0. Lastly, in my equation the value of k is -7. This value gives us the upward or downward shift of the parabola meaning that the vertex moves up or down whatever value k represents. In this case my parabola’s vertex was shifted down by 7 places.

Self-Assessment

During this assignment I was able to show my mathematical learning by using the material learned in order to further my understanding of parabola’s and make assumptions regarding how they’d look without the need of a graph. I demonstrated this throughout my explanations of each different variable and how it influences the parabola’s appearance and equation. In order to both show my mathematical understanding I had to use mathematical vocabulary to fully explain the points needed and my thoughts behind them. For example, I used words like coefficient, compressed, vertex, and parabola to have better descriptions of what exactly I was trying to say in a precise and accurate way. Lastly, in this assignment I used formatting to provide a clear and visually appealing way to present my learning so that others could comprehend it better. In my assignment I specifically used the formatting to apply headings and subheadings to represent changes in topics, colours to coordinate images and words, as well as labelling all images and equations to avoid confusion on what is being described and shown to provide more clarity.