Parent Function
My equation
DESMOS graph
Black parabola: y = x^2
Blue parabola: y = 2(x-2)^2 + 6
a, h and k’s significance in the equation y=a(x-h)^2 +k
In the equation, “a” is the number that controls how wide or narrow the parabola is. Since a>1, the parabola is more narrow compared to the parent function.
(If 0<a<1 or -1<a<0, the parabola would’ve been wider than the parent function)
In the equation, “h” is the number that determines how much the parabola horizontally shifts. If h is equal to (positive) 2, then the vertex with shift right by 2 units.
The parent function has no h value, so there’s no horizontal shift. (It’s vertex is at 0)
In the equation, “k” is the number that determines how much the parabola vertically shifts. If k is equal to (positive) 6, then the vertex with shift up by 6 units.
The parent function has no k value, so there’s no vertical shift. (It’s vertex is at 0)
Self-Assessment
One way that the assignment showed representation of the same mathematical idea in multiple ways is that the equations and parabolas can both give us the vertex. The graph shows what the vertex is based on how much the parabola is shifted, if at all. You can also determine the vertex from “h” and “k” in the equation.
In this assignment, I used mathematical vocabulary to show my understanding of how transforming parabolas differed from their parent function. I used the terms learned in class: vertical and horizontal shift to explain how the parabola had been positioned compared to the parent function. I also used the “<” and “>” symbols to describe why either parabola was wider or more narrow.
I used my formatting to share my information in a clear way by colour-coding and separating each variable’s explanation. That way I can show how each one individually affects the parabola. I also gave each definition their own graph image. “h” and “k” had some added details to the graph to show how they affect shift the parabola.