What is the vertex and the equation of the axis of symmetry of the graph of x^2-6x-7

A second-degree polynomial is always symmetric about the vertical line passing through the vertex.

the vertex of the polynomial

y=Ax^2+Bx+C

is given by

x=-B / (2A)

y=y (b / (2a)) = C-B^2 / (4A)

so the vertex is

(-B / (2a), C-B^2 / (4A))

and the axis of symmetry is x=-B / (2a), i. e. vertical line through vertex.

Here A=1, B=-6, C=-7.

Substitute the values to find the answer.