To convert the given vertex form of the parabola equation [tex]\( y = (x - 3)^2 + 36 \)[/tex] into the standard form, we need to follow these steps:
1. Expand the squared term [tex]\((x - 3)^2\)[/tex]:
[tex]\[
(x - 3)^2 = x^2 - 6x + 9
\][/tex]
2. Substitute the expanded form back into the equation:
[tex]\[
y = x^2 - 6x + 9 + 36
\][/tex]
3. Combine like terms:
[tex]\[
y = x^2 - 6x + 9 + 36
\][/tex]
[tex]\[
y = x^2 - 6x + 45
\][/tex]
So, the standard form of the equation is:
[tex]\[
y = x^2 - 6x + 45
\][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{A. \, y = x^2 - 6x + 45} \][/tex]
