Answer:
(x -3)² -10
Step-by-step explanation:
You want the vertex form of x² -6x -1, found by completing the square.
Completing the square
The square of a binomial is ...
(x -a)² = x² -2ax +a²
The constant in this perfect square trinomial is the square of half the coefficient of the linear term: a² = (-2a/2)²
Application
To complete the square for the given quadratic, the perfect square trinomial must have a constant of (-6/2)² = 9. We can add and subtract 9 to rearrange the quadratic to the desired form.
x² -6x -1
= (x² -6x +9) -1 -9 . . . . . . . +9 -9 was added
= (x -3)² -10
