The vertex form of the equation of a parabola is y=2 (x+4) ^2-7. What is the standard form of the equation.

A. y=2x^2+12x+12

B. x=2y^2+8y+12

C. y=4x^2+4x+8

D. y=2x^2+16x+25

Step-by-step explanation:

To obtain the standard form of the equation of the parabola y=2 (x+4) ^2-7, first perform the indicated operations:

y = 2[x^2 + 8x + 16 - 7], or

y = 2[x^2 + 8x + 9],

or y = 2x^2 + 16x + 18

None of the given possible answers match. The fourth one, D, is closest to the above result, differing only in the constant term (25 versus 18).