A parabola is plotted in a coordinate plane. The x-axis ranges from negative 4 to 4 and the y-axis ranges from negative 6 to 6 in one-unit increments.

Question

Create an equation that models the transformation of y=2x2
to the function in the graph.

(1 point)
Responses

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
y equals 2 left parenthesis x minus 4 right parenthesis sqaured

y=2x2+4

Answer 1

To create an equation that models the transformation of the function \( y = 2x^2 \) based on your description of the parabola, we need to consider how the function is being transformed.

Since you provided a range of x from -4 to 4, and y from -6 to 6, it suggests some horizontal and vertical shifts might be involved.

Let's analyze the provided equations:

1. \( y = 2(x + 4)^2 \): This represents a horizontal shift to the left by 4 units but does not affect the vertical location of the parabola.

2. \( y = 2x^2 - 4 \): This represents a vertical shift downward by 4 units, keeping its vertex at the origin horizontally.

3. \( y = 2(x - 4)^2 \): This represents a horizontal shift to the right by 4 units.

4. \( y = 2x^2 + 4 \): This represents a vertical shift upward by 4 units.

Without the specific graph to reference, if the transformation involves moving the vertex downwards, then:

The best-fit answer, if the graph has been lowered, could be considered as: \( y = 2x^2 - 4 \), because it moves the graph downward without altering the width or direction.

If you have further details about how the parabola is transformed (e.g., does it open upwards? Is it shifted vertically or horizontally?), that could clarify which transformation equation is most appropriate.