The solution would be like this for this specific problem:
-4(y - 5) = (x + 2)²
-4y +20 = x² +4x + 4
-4y = x² +4x - 16
4y = -x² -4x + 16
y = -1/4x² -x + 4
The equation in standard form is y = -1/4x² -x + 4.
I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.