Red Graph: Quadratic parent function 𝑓(𝑥)=𝑥2
Orange Graph: Opens up and is wider 𝑓(𝑥)= 1/3x2
Purple Graph: Opens down and is more narrow 𝑓(𝑥)=-3x2
Black Graph: Shifted to the right 𝑓(𝑥)= (x-3)2
Blue Graph: Shifted down 𝑓(𝑥)=x2-3
Importance of a, h, and k value in my equation
(All statements are based on vertex form of parabola, y=a(x-h)2-k.)
The ‘a’ value is changed and it affects to width of the parabola and tells the which way the parabola is facing; a positive ‘a’ results in an upward opening, while a negative ‘a’ results in a downward opening as shown in the Purple and Red graph. However, If the absolute ‘a’ value is smaller than 1 (|a|>1), the parabola stretches vertically becoming taller and narrower. Additionally, if the absolute ‘a’ value is bigger than 0 and smaller than 1 (0<|a|<1), the parabola widens or becomes compressed in comparison to the parent parabola.
Also a value response to the width of parabola. As ‘a’ value gets smaller, the width of parabola goes smaller, in other word, the shape of the parabola goes more narrow as shown in the Purple and Red graph.
In the Blue and Black graph, they shifted down and right by respectively changing ‘k’ and ‘h’ value. ‘k’ and ‘h’ value indicates the vertex of the parabola. When ‘h’ value is changed, the parabola shifts horizontally, as evident in Black graph. Similarly, changing k value results in vertical transformations of parabola, as demonstrated in Blue graph.
In conclusion, those altering values in equation lead to different transformations of parabola graph.
Self-assessment
1. How did you represent the same mathematical idea in multiple ways in this assignment?
In this assignment, I demonstrated the mathematical idea by using different values for each variable, ‘a, ‘h’, and ‘k’, to show how each affects the shape and direction of the parabola. As I changed the ‘a’ value, the direction and width of the parabola changed. When I modified the ‘h’ value, the parabola shifted to either more right or more left on the x-axis. I have changed the ‘k’ value, which resulted in shifting the parabola either upward or downward.
2. State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.
Some of the mathematical vocabulary I used to demonstrate my understanding of transformations include:
- Parabola
- Equation
- Vertex
- Horizontal and vertical shift
3. How did you use formatting to share your information in a clear and organized way
I used the vertex form of the parabola to present my information in an organized way. This helped me highlight the values that were changed.
