What is the focus of the parabola? y=14x2−x−1

y = 14  ( x^2 - x/14  - 1/14)       complete the square on  x

y  =  14 ( x^2 - x/14 + 1/784 - 1/14 - 1/784)

y = 14 ( x^2 - x/14 + 1/784  -  57/784)

y= 14 ( x - 1/28)^2  -  57/56

We have the form

y = a ( x - h)^2 + k

The focus  is found  at    (  h ,  k + 1/(4a) )  =  ( 1/28 , -57/56 + 1/56) =     ( 1/28 , -57/56 + 1/56)  =  ( 1/28 , -1)

The focus of the parabola y = 14x^2 - x - 1 is at (1/14, -1).  I hope this helps!