My Equation
Parent Function
Blue Parabola y = 3(x+1)2 -1
Green Parabola: y = X2
The Importance of a, h and k in the equation y = a(x-h)2 +k
The significance of “a” in the equation:
The “a” in the parabola equation is what controls how compressed or expanded the parabola is.
The Larger the number “a” is, the more compressed the parabola will be from the parent function.
The smaller the number “a” is between 0 and 1 then the parabola will expand further then the parent function.
In this case “a” is 3 which means the parabola will be compressed more then the parent function.
The significance of “h” in the equation:
The “h” in the equation is what controls the movement from left to right on the parabola.
The “h” in this case is positive which means it will shift to the left, however if it was negative then the parabola would shift to the right.
The significance of “k” in the equation:
The “k” in the equation controls how much the parabola shifts up or down from the parent function.
In this case the “k” is negative 1 which mean the parabola will shift down 1 from the parent function.
Reflection:
I was able to take the idea of the movement of parabolas, by knowing how compressing or expanding, shifting up/down and side to side changes the equation from the parent function. In order to show all the differences that can come from one simple equation, which is the parent function.
In this assignment I was able to use mathematical vocabulary in order to predict how the parabola will look and where the parabola will end up on a graph. For examples, “a” making it compress or expand, “h” making it move side to side, and “k” making it move up and down.
I was able to try and make this assignment clear to understand by using colour coding with text and paragraph backgrounds. As well as different parabola colours from Desmos graphing calculator.