- y = a (x-h)^2 + k 2. y = x^2
My Parabola: 𝑦 =−2(𝑥+6)^2−5 (in blue) Standard Parabola y = x^2 (in black)
- Opening Direction: Downwards
- Vertex: (-6, -5)
- Axis of Symmetry: x = -6
- Domain: All real numbers
- Range: y<= -5
- X-intercept: None
- Y-intercept: y = -77
- Maximum value: -5
My A, H and K and why they made my equation different from the original y = x2 parabola:
The parabola that I got, has all three, an A, an H, and a K. The A value in my parabola, is a negative whole number. This means my parabola will open downwards (because of the negative,) and skinnier (because of the whole number) whereas a positive A would’ve made it open upwards, and a fraction would’ve made it wider.
The H value is what made my parabola move horizontally on the graph, which is why, it’s located to the left at -6 which is what its A.O.S is. It’s K value, is what moved it vertically. This is why my parabola is moved down 5 squares, its range being Y<= -5. Both H & K combined, create the parabola’s vertex (it’s opening point), which in my case is, (-6, -5).
The reason my parabola is different from the original equation, is because the standard equation hasn’t moved around the graph in any way! It’s A is just a positive 1, which is why it opens upwards. It has no H (horizontal shifting) and no K (vertical shifting) values. Which is why, it’s A.O.S is x=0 and range, y>=0. It’s in its “original spot”.
Self-Assessment
In this assignment, I portrayed the same mathematical idea in three different ways. I wrote down the equations, I have a picture of my equation and the standard equation on a graph, and lastly, I explained the importance of how and why some factors of the equation, can change the way that the parabola appears.
I used mathematical vocabulary to explain my understanding while explaining the changes in the two parabolas, and the connection between the A, H and K values in the equation to how all three values visually change the parabola. I was able to explain the connection between the values, and how they contribute to the vertex, and some others.
Some examples of how I used formatting to share my information are; how I separated my content into paragraphs so that it is easier to read, I created headings for the different aspects of this edublog, and used some colour coding to make the information I have more appealing to the eye.