Create an equation that models the transformation of y=2x^2

Question

to the function in the graph. the vertex is at (0,-4)

(1 point)
Responses

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

y=2(x+4)2
y equals 2 left parenthesis x plus 4 right parenthesis sqaured

y=2x2+4
y equals 2 x squared plus 4

y=2x2−4

Answer 1

The original function is \(y = 2x^2\), which has its vertex at (0, 0).

To move the vertex to (0, -4), we need to shift the entire graph down by 4 units. This can be accomplished by subtracting 4 from the function:

\[ y = 2x^2 - 4 \]

So, the correct equation that models this transformation is:

\[ y = 2x^2 - 4 \]

Among the provided options, the correct response is:

y = 2x² − 4