For a point of inflection,
So at (origin)
Now at (2,4) as we have a local maximum, and we must make sure so it is a max and not a min.
Substituting in the values:
(b is gone as it equals zero)
Now, we know that
We know that at , , so you can see .
Now we get .
You know that at , . Simply substitute these values into the equation to find a. Then you can find c.