Aparabola is defined by the equation (x − 5)2 = 12(y + 2). in which direction will the parabola open?

Since the equation is in the form:
(1/a)(y – k) = (x – h)2

Then, the parabola will open either upward or downward. To tell which direction will the parabola open, the coefficient of the term:
(y – k)
must be inspected.

The coefficient is 12 and it is a positive number, therefore, the parabola will open upward.