Equations

1. f(x)=x²

2. y=2x² + 4

3. y=1(x-15)² -5

4. y=1(x+6)²-3

5. y=1(x-6)²-3

6. y=10(x-12)²-11

7. y=7/8(x+12)²-10

Describing My Equations

1. Blue parent function

f(x)=x²

the equation f(x)=x² displays a basic parabola where a=1, h=0, k=0, this mean that vertex would remain (0,0) because there are no vertical or horizontal shifts

2. Purple vertical shift up

y=2x² + 4

In the equation y=2x² + 4, the parabola is shifted upwards by 4 due to the fact that k=4 which is positive implying the parabola is shifted up. in this equation h=0 and a=2 so our vertex is (0,4).

3. Orange vertical shift down

y=1(x-15)² -5

In the equation y=1(x-15)² -5 , the parabola is shifted downwards due to the fact that k=-5 which is a a negative value. In this equation, a=1 and h=-15 meaning the vertex is (15,-5)

4. Red horizontal left shift

y=1(x+6)²-3

In the equation y=1(x+6)²-3, the parabola is shifted horizontally to the left because H=-6 which is a negative value therefore shifting it to the left. the a value is a=1 and the k value is k=-3, our vertex would be (-6,-3).

5. Green horizontal right shift

y=1(x-6)²-3

In the equation y=1(x-6)²-3, the parabola is shifted horizontally to the right because H=6 which is a positive value therefore shifting it to the right. the a value is a=1 and the k value is k=-3, our vertex would be (6,-3).

6. Red dotted line vertical stretch

y=10(x-12)²-11

In the equation y=10(x-12)²-11, the parabola is vertically stretched by 10 because a=10 which is a>0 therefore it is vertically stretched. Also we can see that the parabola is shifted horizontally to the right because H=12 which is a positive value therefore shifting it to the right. The k value is k=-11, which makes our vertex (12,-11).

7. Black line vertical compression

y=7/8(x+12)²-10

In the equation y=7/8(x+12)²-10, the parabola is vertically compressed by 7/8 because a=7/8 which is 0<a<1 therefore it is vertically compressed. Also we can see that the parabola is shifted horizontally to the left because H=-12 which is a negative value therefore shifting it to the left. The k value is k=-10 which makes our vertex (-12,-10).

Communication Core Competency Reflection

I can understand and share information in a clear, organized way. throughout this assignment, I was able to display my thinking both on the graph and in my descriptions of the equation in a way that made it easy to decipher my main points and was well thought out. I was able to show my learning in a way that is clear while also being detailed and demonstrated the ability to process information in an efficient way.

I think about what I am going to convey and to whom I will convey it to. During this assignment especially in my explanation of my equations, I used academic wording that conveyed my information in a professional and clear way. I wrote this assignment in a way that made sense considering it was for academic purposes as well as to be written with academic language.