identify the axis of symmetry, create a suitable?

Question

identify the axis of symmetry, create a suitable
table of values, and sketch the graph (including the axis of symmetry).
y=-x^2+6x-2

Answer 1

dy/dx = -2x+6

-6=-2x

x=3

Ideas:

The axis of symmetry is just the x-coordinate of the vertex, you can get it by completing the square or taking the derivative at the 0 slope.

Answer 2

You can find the axis of symmetry by puting the equation in vertex form:
y = - x^2 + 6x - 2
y = - (x^2 - 6x + 2)
y = - (x^2 - 6x + 9 - 9 + 2)
y = - (x - 3)^2 - 7)
y = - (x - 3)^2 + 7
The axis of symmetry is thus seen to be x = 3.