To convert the vertex form of a parabola to its standard form, we need to follow a series of algebraic steps.
Given the vertex form of the equation:
[tex]\[ y = 2 (x + 3)^2 - 5 \][/tex]
We will expand this equation step-by-step.
1. Expand [tex]\((x + 3)^2\)[/tex]:
[tex]\[
(x + 3)^2 = (x + 3)(x + 3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9
\][/tex]
2. Multiply the expanded expression by 2:
[tex]\[
2(x^2 + 6x + 9) = 2x^2 + 12x + 18
\][/tex]
3. Subtract 5 from the result:
[tex]\[
2x^2 + 12x + 18 - 5 = 2x^2 + 12x + 13
\][/tex]
Therefore, the standard form of the equation is:
[tex]\[ y = 2x^2 + 12x + 13 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{y = 2 x^2 + 12 x + 13} \][/tex]
Thus, the answer choice is B.
