Question

How do you find the axis of symmetry if only given points (0,2) and (6,2)?

Answer 1

Axis of symmetry: `x=3`

Explanation:

Assuming we are talking about a parabola in standard position (with either a vertical or horizontal axis of symmetry:

Since `y=2` has `2` solutions for `x`
the axis of symmetry can not be horizontal.
(A horizontal axis of symmetry has single `x` values for any single value of `y`).

So (based on the assumption (above) the axis of symmetry is vertical
i.e. the axis of symmetry is of the form `x=a` for some constant `a`

and by definition of the axis of symmetry:
`(0,2)` and `(6,2)` must be reflections of each other in this axis
i.e. the `x` values `0` and `6` must be equidistant from the value `a`
`rArr a=3`
and the axis of symmetry is `x=3`

Note that it is possible to have a parabola which has an axis of symmetry that is at an angle to both the X and Y-axis and which passes through the given points, but its axis of symmetry is impossible to determine from the given data.