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=2x^2+4
y equals 2 x squared plus 4

y=2(x−4)^2
y equals 2 left parenthesis x minus 4 right parenthesis sqaured

y=2x^2−4

Answer 1

To determine which equation models the transformation of \( y = 2x^2 \) to a specific function graphed in the coordinate plane, we need to know how the parabola has been shifted or transformed.

If the graph shows that the vertex of the parabola has moved left or right, we will adjust \( x \) in the equation. A transformation of the form \( y = 2(x - h)^2 \) indicates a horizontal shift, where \( h \) is the value to shift right (if \( h > 0 \)) or left (if \( h < 0 \)). Similarly, a vertical shift is reflected in the constant being added or subtracted, giving a form like \( y = 2x^2 + k \), where \( k \) shifts the graph up (if \( k > 0 \)) or down (if \( k < 0 \)).

Without the specific graph, we can evaluate the provided options based on potential transformations:

1. \( y = 2(x + 4)^2 \) - This indicates a shift of the graph 4 units to the left.
2. \( y = 2x^2 + 4 \) - This indicates a vertical shift upwards by 4 units.
3. \( y = 2(x - 4)^2 \) - This indicates a shift of the graph 4 units to the right.
4. \( y = 2x^2 - 4 \) - This indicates a vertical shift downwards by 4 units.

Choose the transformation that corresponds to the graph shown. If, for example, the vertex is shifted to the left by 4 units, then \( y = 2(x + 4)^2 \) would be your answer. If it is shifted upwards by 4 units, then \( y = 2x^2 + 4 \) would be correct, and so on.

Please check the graph to identify its transformations and select the appropriate equation based on that observation.