Equations

f(x)=x² – parent function

The parabola f(x)=x² (in orange) is the parent function of all my parabolas. There is no change to the vertex or shape of this parabola.

f(x)=4/5x²+2 – vertical shift up

The parabola f(x)=4/5x²+2 (in dotted red) has been changed to be wider, and has been vertically moved up. The k value was changed to a 2 which moves the parabola vertically. Making the k value >1 causes the parabola to vertically shift upwards. The a value was also changed. The a value was changed to 4/5 which changes the parabolas shape. Making the a value <1 causes the parabola to widen.

f(x)=7/5x²-4 – vertical shift down

The parabola f(x)=7/5x²-4 (in solid red) has been changed to be wider, and has been vertically moved down. A change in the k value causes the parabola to move vertically. Making the number less than 0 makes the parabola move down. The k value is -4 which means the parabola moved down vertically by 4. The a value was also changed in this parabola. Changing the a value to a number below 1, caused the parabola to widen.

f(x)=-6/10(x-7)²+6 – horizontal shift right

The parabola f(x)=-6/10(x-7)²+6 (in black) has been horizontally moved right, has been changed to open downwards, has been widened, and was vertically shifted up. Changing the h value caused the parabola to horizontally shift. Because I changed the h value to a 7 caused the parabola to shift to the right 7. changing the a value to a negative fraction caused the parabola to open downwards and widen. Changing the k value to 6 caused the parabola to move vertically up 6.

f(x)=-6/10(x+7)²+6 – horizontal shift left

The parabola f(x)=-6/10(x+7)²+6 (in purple) has been moved horizontally left, has been changed to open downwards, has been widened, and was vertically shifted up. Changing the h value caused the parabola to shift horizontally. Because I changed the h value to a negative number, the parabola moved horizontally to the left. I also changed the a value to a negative fraction, making the parabola open downwards and widen. I also changed the k value to a number above 0 which moved the parabola up 6.

f(x)= -8x²-4 – vertical compression

The parabola f(x)= -8x²-4 (in green) demonstrates a vertical compression as well as a vertical shift downwards and has been changed to open downwards. Changing the a value to a number larger than 1 causes the parabola to compress and become more skinny. Changing the a value to a negative causes the parabola to open downwards. The change in the k value to a negative number also caused the parabola to shift vertically downwards.

f(x)=-13/10x²-4 – vertical stretch

The parabola f(x)=-13/10x²-4 (in blue) demonstrates a vertical stretch as well as a vertical shift downwards and has been changed to open downwards. Changing the a value to a fraction or decimal, causes the parabola to stretch. I also made the a value a negative number which causes the parabola to open downwards. The change in the k value also shifted the parabola vertically downwards by 4.

Communication Core Competency Reflection

I can understand and share information in a clear, organized way.

I was able to order my parabolas in a clear and colour coordinated way that is easily understood by peers and teachers. I used different colours to organize my parabolas and wrote clear, distinct paragraphs to showcase their changes and functions.

I think about what I am going to convey and to whom I will convey it to

I am conveying how different changes effect my parabolas and I understand that who I am showcasing this to effects my language towards the topic. I used specific terms to describe the equations that can be easily understood by a math teacher or a peer of mine.