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

1 Answer
Alan P.
Sep 30, 2015

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.

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