+118723 Hi Solveit,
I am glad you are persisting. Persistence is how we learn difficult things. :)
This was one of the constraints of your question
The function has a line of symmetry at x=-3.
Your graph is not correct because the axis of symmetry is x=0 not x=-3
g(x)=ax^2+bx-6a
for the axis to be x=-3
-b/2a must equal -3
-b/2a=-3
b=6a
so t he graph becomes
g(x)=ax^2+6ax-6a
Here is the correct graph
https://www.desmos.com/calculator/ws0izufvrt
NOW if/when (-3,0) is on the function then the function stops being a parabola and becomes a line.
Does a line have an axis of symmetry?
I have never heard anyone say so, but perhaps every perpendicular to a line is an axis of symmetry.
If every perpendicular to a line can be considered tro be an axis of symmetry then (-3,0) could be a point on the function.
SO
I think that you are correct :)
