ANSWER
[tex](2,-10.75)[/tex]
EXPLANATION
The given function is
[tex]y = {x}^{2} - 4x - 7[/tex]
We rewrite this function to obtain,
[tex](y + 11) = {( x- 2)}^{2} [/tex]
We now compare this function to
[tex](y - k) = 4p {( x- h)}^{2} [/tex]
We have
[tex]4p = 1[/tex]
This implies that,
[tex]p = \frac{1}{4} [/tex]
The vertex is (2,-11).
The focus is
[tex](2,-11+ \frac{1}{4} )[/tex]
[tex](2,- \frac{43}{4} )[/tex]
[tex](2,-10.75)[/tex]
