Comparison of Quadratic Form and Parabola Standard Form on a graph
Red Parabola y=x2 (My Equation) Blue Parabola y=a(x-h)2+k
Graphing a Parabola of y=x2 is the standard form. The equations that determine a parabola are called quadratic functions. The graph of y=a(x-h)2+k is similar to y=x2 but is shift left or right due to the value of “k.
There are three values that have significance in the equation which are “a”, “h”, and “k.” The value of “a” determines the shape of the parabola, it affects the way the parabola is facing either opening upwards or downwards on the graph.
My parabola has an “a” value of 1/4
It indicates that “a” is greater than “0” but less than 1 (0<a<1). As the graph of the parabola shows that it opens wider. For further detail, when “a” is less than “0” (a < 0), the parabola will be opening downwards on the graph. If the value of “a” is greater than “0” the parabola will open upwards.
The value of “h” indicates a horizontal shift on the graph. Where it determines how far to the right or left the parabola is facing starting at the point of (0,0). In my equation, the value of “h” is positive 5 (+5). Meaning the parabola will be shifted towards the left of the graph, due to the sign changing the opposite sign. Therefore, indicates the value of “x” of the vertex. (-5, 0). The standard form of graphing a parabola has a vertex of (0,0).
The value of “k” in the quadratic form indicates a vertical shift on the graph. The vertical shift determines how far it moves upwards or downwards on the graph. My equation has the value of negative 7 (-7), meaning it is shifted vertically downwards 7 squares. If the value of “k” is negative the vertical shift will move downwards towards the negative y – axis. When the value of “k” is a positive number the vertical shift
Self-Assignment
In my assignment of Graphing Parabola, I represented my quadratic equation in three different aspects for mathematical understanding. To help me have a better understanding of Quadratic equations, I created a visualization aspect to the assignment by using demos. By adding two similar equations to signify how they’re different from one another. I used numbers from the equations to describe what each value means and how it contains proper information for the graph. How each value indicates a specific function on how the parabola forms on the graph. To further explain my observations, I clarified by using my own words and vocabulary that represented quadratic functions.
An example when using mathematical vocabulary to demonstrate my understanding is describing the value of “k.” Where it signifies how the vertical shift moves up/downwards towards the negative/positive y- axis.
To organize my learning about the information about this assignment, I formatted my data and statistic in paragraph form. By organizing each topic in its own subject and adding significant detail on that certain topic.