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