My equation:
My graph:
In the Parabola equation vertex form y=a(x−h)2+k, the ‘a’ value which is the coefficient of the equation, determines whether the parabola will be wider or thinner and whether it is facing in up or down direction. For my equation, the -1/4, which is a fraction, made the parabola wider. It also opened downwards because my ‘a’ value is negative.
The ‘h’ value represents the axis of symmetry. x=h It is one of the vertex in the parabola and it determines the horizontal shift (whether it shifts to the left or right of the graph from x=0). For my equation, (x+1)^2 is the x-intercept of the vertex and this tells me that it moves to the left because when ‘h’ is added from x (x + h), the parabola shifts to the left side of the graph.
The ‘k’ value represents the vertical shift of the parabola (how far up or down the graph shifted from y=0). It is also the other number in the vertex which represents the range. In my equation, -4 which is the ‘k’ value, shows that it is the maximum value of the parabola. It shifted 4 units downwards because it is a negative.
The vertex in my equation is shown in the blue parabola, (-1,-4). The vertex of the original equation is (0,0).
Self-Assessment
- Give an example from this assignment where you represented the same mathematical idea in three different ways? (for example, as a graph, an equation and in words)
I was able to discuss the significance of the vertex form of a parabola equation and apply it to my own parabola equation. The graph image shows how the two parabolas differ from one another. I incorporated mathematical terms into my short paragraphs as well. To show the parabolas’ maximum and minimum, I included the range in the graph.
2. Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.
I was able to use words such as maximum value, ‘a’ value, shift, and vertex to explain my parabola.
3. Give an example from this assignment where you used formatting to share the information in a clear and organized way.
In my graph, I essentially used four different color types—green, black, blue, and violet—to indicate both the original parabola’s range and my own parabola’s range. I ordered my parabola explanation as best I could by going over each step from “a” to “k.”