Parabolas and Their Transformations

Parent Function: y=x²

Vertex: (0,0)

1. Equation A: y=2(x – 6)²

Vertex: (6,0)

Transformation: This parabola has been shifted 6 units to the right, and vertically compressed by a factor of 2, making it narrower.

2. Equation B: y=-2x² + 7

Vertex: (0,7)

Transformation: This parabola opens downward because of the negative coefficient and has been vertically compressed by a factor of 2. It is shifted 7 units up.

3. Equation C: y=1/7(x + 5)² – 6

Vertex: (-5,-6)

Transformation: This parabola has been shifted 5 units to the left and 6 units down. It is vertically stretched by a factor of 1/7, making it wider.

4. Equation D: y=-1/6(x – 8)² – 3

Vertex: (8,-3)

Transformation: This parabola open downward because of negative sign and is shifted 8 units to the right and 3 units down. It is vertically stretched by a factor of 1/6, making it wider.

Assessment

1. How did you represent the same mathematical idea in multiple ways in this assignment?

• I used Desmos to graphically represent the transformation of the graphs.

2. State of the relevant mathematical vocabulary words you used to demonstrate your understanding and their definitions. State where you found the definitions (your own memory, class notes, online).

• Vertex: the highest or lowest point of a parabola, located at (h,k). (Class notes)
• Parabola: A U-Shaped curve that is the graph of a quadratic function. (Memory)
• Transformation: The process of shifting, reflecting or stretching/compressing a graph. (Online)

3. How did you use formatting to share your information in a clear and organized way?

• I organized the content by clearly listening each equation and labeling each vertex. I also made it easier to understand by explaining all the elements where the graph is transformed.