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

Apr 22, 2015

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.

Apr 22, 2015

Assuming the parabola is in "standard" position (i.e. not rotated) and has a formula $y = a {x}^{2} + b x + c$

Then if the vertex is at $\left(6 , 1\right)$
the axis of symmetry is a vertical line through $\left(6 , 1\right)$
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).