Write the equation for a hyperbola that passes through the point (‐ 2, ‐ 3)?

The equation of hyperbola can vary much from simple to complex equation. Since the information given from this question is not many, the equation probably was the simple one. 
Assuming that the hyperbola formula is y= x^2 +b, then the value of b where x=-2 and y=-3 would be:
y= x^2 +b
-3= (-2)^2 +b
-3= 4+b
b=-3 -4= -7

The equation would be: y= x^2 -7