Y=1/6f(x+17) what is the domain and range

Since x can be any real number the domain is (-infinity,infinity)

 

To find the range we need to find the vertex of the parabola which is at (-b/2a , y)

-b/2a would be 2/2 = 1 ... so find the y value at x = 1

12 - 2(1) - 15 = 1-17 = -16

So the vertex is at (1,-16)

Since the parabola opens upward from that point the minimum value of the range is y = -16

The range would include the point -16 so it is actually

R = [-16,infinity)