Answer:
(1, -2)
Explanation:
You want the coordinates of the vertex of the parabola defined by ...
Vertex form
We can add and subtract the square of half the x-coefficient to put the equation in vertex form:
y = x² -2x -1
y = x² -2x +(-2/2)² -1 -(-2/2)²
y = (x² -2x +1) -1 -1
y = (x -1)² -2
Comparing this to the vertex form equation ...
y = (x -h)² +k . . . . . . parabola with vertex (h, k)
we see that the vertex is ...
(h, k) = (1, -2)
The coordinates of the vertex are (1, -2).
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