Question

If the vertex of a parabola is (6,1) what is the equation for the axis of symmetry?

Answer 1

The axis of symmetry runs through the vertex.

So, if it is a vertical parabola (one that opens up or down) then the axis of symmetry is the vertical line through the vertex.

If it is a horizontal parabola (one that opens right or left) then the axis of symmetry is the horizontal line through the vertex.

If it is a slant (or skew) parabola, the the axis of symmetry is a slanted line through the vertex.

Answer 2

Assuming the parabola is in "standard" position (i.e. not rotated) and has a formula `y =ax^2+bx+c`

Then if the vertex is at `(6,1)`
the axis of symmetry is a vertical line through `(6,1)`
and since a vertical line has the form `x = k` for some constant `k`

the equation for the axis of symmetry is
`x=6`

(Note that if the parabola has been rotated there is no way from the given information to establish the axis of symmetry).