ANSWER
[tex](2,- 1)[/tex]
EXPLANATION
The given parabola is
[tex]y = \frac{1}{4} {x}^{2} - x - 1[/tex]
We need to write this parabola in the vertex form by completing the square,
[tex]y = \frac{1}{4} ( {x}^{2} - 4x) - 1[/tex]
[tex]y = \frac{1}{4} ( {x}^{2} - 4x + 4) - \frac{1}{4} \times 4 - 1[/tex]
[tex]y = \frac{1}{4} (x - 2 )^{2} - 2[/tex]
[tex] {(x - 2)}^{2} = 4(y + 2)[/tex]
The vertex is
(2,-2)
The focal length is
[tex]p = 1[/tex]
The focus is
[tex](2,-2 + 1)[/tex]
[tex](2,- 1)[/tex]
