we have the function
ƒ(x) = 1∕2(x – 3)^2 – 6
This function represents a vertical parabola open upward
so
The vertex represents a minimum
The vertex is the point (3,-6)
the y-intercept is
For x=0
y=-1.5 -------> y-intercept is (0,-1.5)
Looking at the options
the answer is option B