ANSWER
The vertex is (1,-3)
EXPLANATION
The given parabola has equation:
[tex] {y}^{2} + 6y + 8x + 1 = 0[/tex]
We group the variables to obtain:
[tex]{y}^{2} + 6y = - 8x - 1 [/tex]
We complete the square to get,
[tex]{y}^{2} + 6y + {3}^{2} = - 8x - 1 + {3}^{2} [/tex]
[tex] {(y+ 3)}^{2} = - 8x +8[/tex]
[tex] {(y+ 3)}^{2} = - 8(x -1)[/tex]
The vertex is of the parabola is (1,-3)
