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

Question

Isaiah Anthony · Accepted Answer

Axis of symmetry: #x=3#

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.

Savannah Anderson · Answer

undefined To find the axis of symmetry when given two points, first, calculate the midpoint between the x-coordinates of the two points. This will give you the x-coordinate of the axis of symmetry. The equation of the axis of symmetry is x = (x₁ + x₂) / 2. So, in this case, the x-coordinate of the axis of symmetry is (0 + 6) / 2 = 3. Therefore, the axis of symmetry is the vertical line x = 3.