Question

If the vertex of a parabola is (5,3) what is the equation for the axis of symmetry?

Answer 1

With informaion that vertex is `(5,3)`, we cannot say anything about axis of symmetry.

Explanation:

With vertex as `(5,3)`,

we can either have a parabola such as `y=2(x-5)^2+3`, whose axis of symmetry is `x=5`

graph{y=2(x-5)^2+3 [-0.81, 9.186, 1.24, 6.24]}

or `x=(y-3)^2+5`, whose axis of symmetry is `y=3`

graph{x=(y-3)^2+5 [-0.29, 9.71, -0.12, 4.88]}

Hence, just because vertex is `(5,3)`, we cannot say anything about axis of symmetry.