Red Parabola
This parabola is the parent function. The vertex is (0,0) and it’s equation is y=x².
Blue Parabola
The equation for this function is y= 2x²+3, vertex= (0,3)
Green Parabola
The equation for this function is y= -(x+4)²-1, vertex= (-4,-1)
Black Parabola
The equation for this function is y= 4(x+5)²+2, vertex= (-5,2)
Purple Parabola
The equation for this function is y= ⅓(x-5)²-3, vertex= (5,-3)
Paragraph
The a, h, and k are all significant in a parabola’s function. They help us to identify how much has a parabola shifted both laterally and vertically, as well as if it is vertically slim or vertically . The parent function is placed in the centre of the graph, and is a point of reference for the diverse parabolas that have been featured in my graph. For the blue parabola it it has been altered as the a value is 2, and the k value is 3. It has been shifted vertically upwards, but the axis of symmetry (line that splits the parabola into two) remains 0. What is also noticeable about the parabola is that it is slimmer and skinnier than the parent function. This is because when a>1, this causes the parabola to vertically stretch. The other 3 parabolas that I have created all share a singular similarity, which is that they are all have an a vertex in which the x and y values are are greater or less than zero. The black parabola is the most vertically stretched, as it has the greatest a value. It’s axis of symmetry is -5, but in the equation it is written as y= 4(x+5)²+2. This is because whatever the x value is in the vertex, when plugged in the equation must be the opposite value. The green parabola is the odd one out of all the parabolas, as it is facing downwards. This is because the a value has become negative, and when this occurs the parabola opens downwards. This just shows how significant the a value can be, as it displays how placing a negative symbol can alter the outlook of a parabola’s function. The purple parabola is the only one that has x intercept [(2,0) and (8,0)], as well as y intercept [(0,5.3)]. It is the most vertically compressed parabola as the a value is less than one (0<a<1). With all parabolas that display fractions where the numerator is less than the denominator, it will be wider than other parabolas, including the parent function.
Self Assessment
How did I represent the same mathematical idea in multiple ways in this assignment?
I represented it by changing and showing how the parabola is altered by plugging in different vertexes, as well as a values. I used the same equation repeatedly, and it shows what a drastic difference there can be when certain numbers are entered into the a, h, and k values. I showed this by entering different equations and observing the changes that these parabolas possess compared to the parent function.
What mathematical vocabulary did I use in my assignment?
I feel like I used multiple mathematical vocabulary words throughout my assignment. For example, axis of symmetry, vertex, x and y axis, vertical stretch, and vertical compression just to name some. I had gained this vocabulary from the notes, as the lessons were straight forward and introduced these concepts clearly. While working on this assignment, I constantly referred to the notes in our class notebook to assure myself that the vocabulary I was using was correct and made sense to the audience observing this assignment.
How did I format my assignment to share my information clearly?
When I took the screenshot of my graph, I made sure it was clear and that the lines were not disorganized and easy to see. I distinguished each parabola by giving each one a different colour so that the reader can look at the description of the equation, and know which one belong to what parabola. I also bolded my questions to make sure that it doesn’t get mixed up with my answers. I feel like this assignment is well developed and organized so that it is easy for whoever is observing my assignment to follow, I have done it this way in past edublogs and received positive feedback for the format.