Question
Create an equation that models the transformation of y=2x2
to the function in the graph.
(1 point)
Responses
y=2x2+4
y equals 2 x squared plus 4
y=2(x+4)2
y equals 2 left parenthesis x plus 4 right parenthesis sqaured
y=2x2−4
y equals 2 x squared minus 4
y=2(x−4)2
to the function in the graph.
(1 point)
Responses
y=2x2+4
y equals 2 x squared plus 4
y=2(x+4)2
y equals 2 left parenthesis x plus 4 right parenthesis sqaured
y=2x2−4
y equals 2 x squared minus 4
y=2(x−4)2
Answers
GPT-4o mini
To model the transformation of the function \( y = 2x^2 \) to another function based on the graph, we need to consider what type of transformations (shifts, stretches/compressions, or reflections) are being performed.
Here are the given options analyzed:
1. **\( y = 2x^2 + 4 \)**: This represents a vertical shift upwards by 4 units.
2. **\( y = 2(x + 4)^2 \)**: This represents a horizontal shift to the left by 4 units, and it also retains the same vertical stretch.
3. **\( y = 2x^2 - 4 \)**: This represents a vertical shift downwards by 4 units.
4. **\( y = 2(x - 4)^2 \)**: This represents a horizontal shift to the right by 4 units.
To determine which equation represents the transformation represented in the graph accurately, you would need to know the specifics of the graph after transformation. If you provide more details about how the original graph has been transformed, I can help you choose the correct equation!
Here are the given options analyzed:
1. **\( y = 2x^2 + 4 \)**: This represents a vertical shift upwards by 4 units.
2. **\( y = 2(x + 4)^2 \)**: This represents a horizontal shift to the left by 4 units, and it also retains the same vertical stretch.
3. **\( y = 2x^2 - 4 \)**: This represents a vertical shift downwards by 4 units.
4. **\( y = 2(x - 4)^2 \)**: This represents a horizontal shift to the right by 4 units.
To determine which equation represents the transformation represented in the graph accurately, you would need to know the specifics of the graph after transformation. If you provide more details about how the original graph has been transformed, I can help you choose the correct equation!