Question
Create an equation that models the transformation of y=2x2 to the function in the graph.
(1 point)
Responses
A. y=2x2+4
B. y=2(x−4)2
C. y=2(x+4)2
D. y=2x2−4
(1 point)
Responses
A. y=2x2+4
B. y=2(x−4)2
C. y=2(x+4)2
D. y=2x2−4
Answers
GPT-4o mini
To find the equation that models the transformation of the function \( y = 2x^2 \) to a new function shown in a graph, we need to identify what type of transformations are applied (e.g., shifts, stretches, reflections).
Since I don’t have access to the specific graph you are referring to, I can provide a guideline to derive the correct option based on common transformations:
1. **Vertical Shifts**: If the graph has moved up or down, you would add or subtract a constant from the function:
- Up: \( +k \)
- Down: \( -k \)
2. **Horizontal Shifts**: If the graph has moved left or right, you would change \(x\):
- Left: \( (x + h) \)
- Right: \( (x - h) \)
3. **Vertical Stretches/Shrinks**: The coefficient before \( x^2 \) indicates vertical stretching if greater than 1 or shrinking if between 0 and 1.
4. **Reflections**: If the graph flips over the x-axis, a negative sign is added before \( 2 \).
With these transformations, you can analyze options from A to D:
- A: \( y = 2x^2 + 4 \) (vertical shift up)
- B: \( y = 2(x - 4)^2 \) (horizontal shift right)
- C: \( y = 2(x + 4)^2 \) (horizontal shift left)
- D: \( y = 2x^2 - 4 \) (vertical shift down)
Without the graph, I cannot determine which transformation applies. However, you can use this information to match the changes in the graph to determine which equation correctly reflects those transformations.
If you describe the transformation reflected in the graph (e.g., shifting up/down, left/right), I can help you select the right choice.
Since I don’t have access to the specific graph you are referring to, I can provide a guideline to derive the correct option based on common transformations:
1. **Vertical Shifts**: If the graph has moved up or down, you would add or subtract a constant from the function:
- Up: \( +k \)
- Down: \( -k \)
2. **Horizontal Shifts**: If the graph has moved left or right, you would change \(x\):
- Left: \( (x + h) \)
- Right: \( (x - h) \)
3. **Vertical Stretches/Shrinks**: The coefficient before \( x^2 \) indicates vertical stretching if greater than 1 or shrinking if between 0 and 1.
4. **Reflections**: If the graph flips over the x-axis, a negative sign is added before \( 2 \).
With these transformations, you can analyze options from A to D:
- A: \( y = 2x^2 + 4 \) (vertical shift up)
- B: \( y = 2(x - 4)^2 \) (horizontal shift right)
- C: \( y = 2(x + 4)^2 \) (horizontal shift left)
- D: \( y = 2x^2 - 4 \) (vertical shift down)
Without the graph, I cannot determine which transformation applies. However, you can use this information to match the changes in the graph to determine which equation correctly reflects those transformations.
If you describe the transformation reflected in the graph (e.g., shifting up/down, left/right), I can help you select the right choice.