Is the only way to solve these kinds of questions to graph it and see visually? (Grade 11 beginner)

Question

pottersheep · Answer

For exp.  graph y = x^2, y=(2x)^2 , y = (1/2x)^2 find invariant points

pottersheep · Answer

would I have to graph those to find the invariant points?

anonymous · Answer

do you know the definition of an invariant point?

mathteacher1729 · Answer

How are "invariant points" defined?

pottersheep · Answer

Points that are the same?

anonymous · Answer

the same as what?  Look it up.

mathteacher1729 · Answer

So basically you have y = (kx)^2 for k = (some range of numbers) and you want to find the values of x which always yield the same values of y, regardless of the values of k?  If yes, the only point is (0,0) for this graph.  (see attached).

mathteacher1729 · Answer

made with: Geogebra --> http://www.geogebra.org

pottersheep · Answer

a fixed point = invariant point