My Equation was: y=-2(x-6) 2 +1 [This is in vertex form: y=a(x-h) 2 +k] The Parent Function was: Y=x2
Significance of “A” “H” and “K”
“A” is significant to my parabola because it determines which way my parabola will open up. Because my “A” value is -2, my parabola opens downwards as oppose to a positive “A” value which would open upwards. The “A” value also affects the vertical shape of the parabola (how stretched or shrunk it is). If “A” is between -1 and 1, the parabola is stretched. If “A” is less than -1 or greater than 1 the parabola is compressed. In my parabola, the “A” value causes the parabola to be compressed because A=2. This means that my parabola is compressed.
“H” represent the horizontal shift in my graph from X=0. In the case of my parabola, the “H” value of 6 has caused the parabolas vertex to move six times to the right (in the positive “x” direction).
“K” represents the vertical shift in my graph from y=0. My equation has a “x” value of 1 which means it moves up once into the positive “y” direction
The “H” and “K” values are the coordinates for the vertex on my parabola.
Self Assessment
I represented the same mathematical idea in multiple ways by showing the effects of the “H” and “K” values and then made the connection that those values are the coordinates for the vertex of my parabola. This helped me significantly increase my understanding of the relation between equations in vertex form and parabolas on a graph.
I used mathematical vocabulary to show my understanding when I used the positive/negative “x” and “y” directions to help show my understanding of the equation values to the graph.
I used formatting to display my graph, parabola, parent function and equation in a neat and easy to follow image that clearly shows which equation belongs to which graph. I also utilized brackets and quotation marks to ensure that all of my equations and variables are not mixed into my writing in a way that could confuse a reader.