To convert the equation [tex]\( y = 2(x + 4)^2 - 7 \)[/tex] from vertex form to standard form, follow these steps:
1. Expand the binomial:
Start with the binomial part [tex]\((x + 4)^2\)[/tex].
[tex]\[
(x + 4)^2 = x^2 + 8x + 16
\][/tex]
2. Distribute the coefficient 2:
Multiply each term inside the binomial by 2.
[tex]\[
2(x^2 + 8x + 16) = 2x^2 + 16x + 32
\][/tex]
3. Combine the constants:
Now, incorporate the constant term [tex]\(-7\)[/tex] outside the binomial.
[tex]\[
y = 2x^2 + 16x + 32 - 7
\][/tex]
Simplify this by combining the constant terms [tex]\(32\)[/tex] and [tex]\(-7\)[/tex].
[tex]\[
y = 2x^2 + 16x + 25
\][/tex]
So, the standard form of the equation is:
[tex]\[
y = 2x^2 + 16x + 25
\][/tex]
This corresponds to option A:
[tex]\[
\boxed{y=2 x^2+16 x+25}
\][/tex]
