What is the axis of symmetry for y=-1/3(x+2)squared +5

Hello from MrBillDoesMath!

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