When transforming parabolas, the a, h and k values are significant because they determine how the parabola looks on a graph. What makes the blue parabola different from the parent function, (black parabola) is that the h value is 4 which makes the parabola shift 4 spaces to the right and since the k value is -5, the parabola shifted down by 5 spaces. The green parabola’s a value is -1/4 making the parabola open downwards, and since the absolute value of -1/4 is less than 1 and is a negative number, the green parabola opens down and is vertically compressed appearing shorter and wider than the parent function. The green parabola also has a h value of -3 making the parabola shift along the x-axis to the left by 3 spaces. The purple parabola has an a value of 3 making the parabola open up because it is a positive number and since 3 is greater than 1the parabola appears vertically stretched and narrower then the parent function. The purple parabola’s h value, -5 made it shift 5 spaces to the left while the k value, -2 made it shift 2 spaces down. The red parabola has a a value of -4 making it open down because it is a negative number and the a value also tells us that the parabola looks vertically stretched because the absolute value of -4 is greater than 1. The h value is 4 which tells us that the parabola is shifted to the right by 2 spaces. It also tells us that the axis of symmetry of this parabola is x=4 which is the same as the blue parabola. The k value of the red parabola is 3 which tells us that it has vertically shifted 3 spaces.

Self Assessment

I represented the same mathematical idea in multiple ways through this assignment by having a visual representation of a graph on Desmos to show parabolas and their transformations. I visually showed how a parabola can appear differently from a parent function on the graph by having the parent function in black while the parabolas I chose were different colors to represent the different kinds to show how they transformed. I also wrote a paragraph explaining why the a, h and k values are significant for transforming each of the chosen parabolas. I described how these values made each of the parabolas different from the parent function and how they would move.

I used relevant math vocabulary to demonstrate my understanding of the concepts and definitions of the words. One mathematical word I used in the assignment was “parent function” which is the simplest form of a quadratic function or before it has gone through any transformations. I remembered this term when going over notes in class. Another mathematical term I used is “vertical stretch” or “compress”. These terms means when the absolute value of a is greater or less than 1 the parabola will appear taller and narrower or shorter and wider. I got this definition from class notebook. “Axis of symmetry” is another mathematical term I used. It means the imaginary line that runs through the vertex of the parabola with each side being symmetrical. I remembered this term from notes in class.

I used formatting to share information in a clear and organized way in this assignment by having a picture of the graph I made on Desmos big enough to clearly see all the parabolas chosen. I sized the image of the graph to fit the edublog in a neat way. The vertex of each parabola was labeled so it is clear. I listed the functions of the parabolas with the color of the parabola next to it to make it clear which function was for which parabola. For my paragraphs I used bolding and quotations to make it clear of what values I was talking about. I used headings to separate my paragraph about transforming parabolas from my self assessment.