# My Parabola: 𝑦= −2(𝑥+1)² −7

## The Signifigance of A:

The signifigance of A in a parabola determines if the parabola is facing up, or facing down. It also determines how wide, or how narrow the parabola will be. In my parabola, the A value is -2, meaning the parabola is facing down, and is realtively narrow. When the value of A is a large positive number, it becomes narrow, and when the value of A is a very small positice number, (fraction), it becomes wide. When the value of A is negative, it opens downwards. Compared to the standard parabola y=x², my parabola y=-2(x+1)²-7, has flipped upside down, and has become slightly more narrow, due the the A value being -2.

## The Signifigance of H:

The signifigance of H in a parabola represents a horizantal shift, meaning how far right, or how far left the parabola has shifted. The value of H in my parabola is -1, meaning -1 is the horizantal (x) coordinate of the vertex. Since H is the X coordinate of the vertex, it is also the axis of symmetry. Compared to the standard parabola y=x², my parabola y=-2(x+1)²-7, has the axis of symmetry x=-1, whereas the axis of symmetry for the standard parabola is x=0. This means that my parabola has shifted 1 to the left compared to the standard parabola.

## The Signifigance of K:

The signifance of K in a parabola represents a vertical shift, meaning how far up, or how far down the parabola has shifted. In my parabola, the value of K is -7, meaning the entire parabola has shifted down 7 squares. The value of K also represnts the Y coordinate of the vertex. My vertex is (-1,-7) whereas the standard parabola’s vertex is (0,0). K also represents the mininum/maxinum value, in my vertex -7 is the maxinum value, whereas in the standard parabola’s vertex, it has a mininum value of 0.

## Give an example from this assignment where you represented the same mathematical idea in three different ways:

I represented the same mathematical idea in three different ways within this assignment. I showcased my parabola in a graph form using Desmos, which is a great visual representation of this assignemnt. Another way I showcased my parabola was simply by stating my equation, y=-2(x+1)²-7. In stating my equation, I was able to dissect different elements of the equation that lead to the third way I represented my parabola. In explaining the signifgance of A,H, and K, I was able to represent my parabola was by using mathematical vocabulary and breaking down each part of the equation.

## Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding:

I used mathematical vocabulary to demonstrate my understanding when I was explaing the signifgance of A, H, and K. I used terms that we have learned so far in this unit like, parabola, vertex, axis of symmetry, as well as a few others. In using these mathermatical terms, I further showcased that I have a good understanding of chapter 3.

## Give an example from this assignment where you used formatting to share the information in a clear and organized way:

I used formatting to share the information in a clear and organzied way by taking my time with this Edublog. I made sure that both of my graphs were clear and easy to read by making them large and at the top of the page. I changed the background of both graphs to a black colour, as I found the white colour was harder to see. I added headings above each question to make it organzied and clear what I was discussing. I added colour to these headings to make them stand out. Before posting this, I made sure that I previewed it to ensure my layout was organized. In using my organizational skills, I formated this assignment in such a way where all the information was clear and concise.