Question

What are the coordinates of the vertex of the parabola y = x2 - 2x - 1?

Answer 1

(1, -2)

Explanation:

You want the coordinates of the vertex of the parabola defined by ...

• y = x² -2x -1

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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