Given g(x)=x^2-7x+1/4 show that the least possible value of g(x) is -12

The least vale of the function would be the vertex. To find the vertex first find the x value by using x= -b/2a
x=7/2 or 3.5
Now plug this in for x to find the y value.
y = (7/2)^2 -7(7/2) + (1/4)
y = (49/4) -(49/2) + (1/4)
y = (49/4) -(98/4) + (1/4)
y = (-48/4)
y = -12
The vertex is (3.5,-12)
The minimum (or max) of a function is the y value of the vertex so the min value is -12