ANSWER
[tex](1,-2)[/tex]
EXPLANATION
The given quadratic equation is:
[tex]y = - {x}^{2} + 2x - 3[/tex]
The axis of symmetry of this parabola is
[tex]x = 1[/tex]
This is the also the x-coordinate of the vertex.
To find the y-coordinate of the vertex, substitute x=1 into the equation.
[tex]y = - {(1)}^{2} + 2(1)- 3[/tex]
[tex]y = - 1 + 2 - 3[/tex]
[tex]y = - 2[/tex]
The vertex is
(1,-2)
