Hello from MrBillDoesMath!
Answer:
x = -2
Discussion:
Consider the simpler equation y = 1/x^2. The line of symmetry is the vertical asymptote x = 0. In our problem the factor 1/(x+2) ^2 displaces the curve y = 1/x^2 2 units to the left. In short, the axis of symmetry of our equation is x = -2. (Note the 1/3 and 5 constants do not impact the axis of symmetry. See attachments, whose y value starts at 5,
I am interpreting the original equation as
y = ( (1/3) * (1/(x+2)^2) ) + 5
Thank you,
MrB
