My equation:

The Significance of a, h, and k in the Equation of a Parabola

In most equations of a parabola, there are three main components, a, h, and k, “a” is significant because it can determine if the parabola opens upward (+a) or downward (-a) as well as if the parabola is narrow (a>1) or wide (0<a<1). My equation’s “a” value is positive 1/4 therefore my parabola opens upwards, and is wide. The significance of “h” is that it affects the horizontal shift of the parabola, if the “h” value is negative the parabola would shift to the right side, if the “h” value is positive the parabola would shift to the left side. In my equation my “h” value is positive 5 which causes my parabola to shift 5 spaces to the left. The importance of “k” is because it determines the parabola to shift down (-k) or to shift up (+k), my “k” value is negative 7 which is why my parabola is down 7 spaces. The main differences between my parabola and the standard parabola is the placement on the graph, my parabola is shifted to the left as well as shifted down while the standard parabola is shifted to the middle and starts at 0; the standard equation actually doesn’t have an “h”and “k” value it equals 0 and the “a” value equals positive 1 while my equation does have an “h” and “k” value.

Self-Assessment

In this assignment I represented the same mathematical idea in three different ways, in words, numbers/equations, and as a graph. I explained in words by writing the significance of a,h, and k and how it affected my parabola, I wrote out the equations and inspected them, and I also used desmos to represent the equations on a graph. An example where I used mathematical vocabulary in this assignment is when I explained the importance of a,h, and k and what they meant for my parabola. In this assignment I used formatting to share the information in a clear and organized way by using colours to differentiate the equations, I also used headings to properly separate each section so it could be easy to read and understand.