To convert the given equation of a parabola from its vertex form to standard form, we need to follow these steps:
1. Start with the vertex form:
[tex]\[
y = (x + 5)^2 + 49
\][/tex]
2. Expand the squared term [tex]\((x + 5)^2\)[/tex]:
[tex]\[
(x + 5)^2 = x^2 + 10x + 25
\][/tex]
3. Substitute the expanded form back into the equation:
[tex]\[
y = x^2 + 10x + 25 + 49
\][/tex]
4. Combine like terms to simplify the equation:
[tex]\[
y = x^2 + 10x + 25 + 49
\][/tex]
[tex]\[
y = x^2 + 10x + 74
\][/tex]
So the standard form of the equation is:
[tex]\[
y = x^2 + 10x + 74
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{B. \, y = x^2 + 10x + 74}
\][/tex]
