To find the interval(s) over which the function -3x^2+12 is decreasing, we need to find the critical points of the function and test the sign of the derivative on either side of these points.
The derivative of the function -3x^2+12 is -6x.
Setting the derivative equal to zero to find the critical points:
-6x = 0
x = 0
Testing the sign of the derivative on either side of x = 0:
-6x is negative for x > 0, meaning the function is decreasing on the interval (0, infinity).
-6x is positive for x < 0, meaning the function is increasing on the interval (-infinity, 0).
Therefore, the interval over which the function -3x^2+12 is decreasing is (0, infinity).