1. The variable “4” affects the steepness of the parabola. Specifically, the larger the value of “4”, the more compressed the parabola will be, and the smaller the value of “4”, the more stretched the parabola will be.
2. The variable “(x + 1)” represents the horizontal shift of the parabola. Specifically, the “1” in the expression “(x + 1)” means that the vertex of the parabola is shifted to the left by one unit.
3. The variable “2” represents the vertical shift of the parabola. Specifically, the “2” in the equation means that the vertex of the parabola is shifted upward by two units.

Overall, changing the values of these variables will change the shape and position of the parabola. For example, increasing the value of “4” will make the parabola steeper, shifting the vertex to the right of the origin will move the entire parabola to the right, and increasing the value of “2” will shift the entire parabola up.

1. Give an example from this assignment where you represented the same mathematical idea in multiple ways?

I represented the same mathematical idea in 3 different ways. I represented the math equation i got by putting it into a graph and having a visual representation. Also the equation itself is a representation of the different elements of the graph. And finally I talked and explained how each part of my equation effects the graph ion my own words.

2. Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.

I used mathematical vocabulary when explaining how the different value of “a” whether it be a bigger or smaller value contributed to the graph being “compressed” or “stretched”. I also used mathematical vocabulary when explaining how the “h” and “k” value of an equation can determine the vertical or horizontal shift of the parabola.

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

I went on canva to try to project my understanding in a fun and organized way, but found it to be difficult to use. In the end I shared my information by pointing arrows to the two different graphs and also sharing my understating of the different values of an equation and how it can effect the parabola in steps.