C1 - Differentiation :)

...

Can someone guide me in the right direction with the following question:

The curve with equation $y=ax^2+bx+c$ passes through the point (1,2). The gradient of the curve is zero at the point (2,1). Find the values a,b and c.

umm what I have done so far, not sure if it is right..

2= a+b+c
dy/dx= 2ax+b
When 2 is subbed in the gradient = 0?
4a+b=0

Is that right?? What do I do next?
Thanks

You also know that (2,1) is a point on the curve, so you can set up a third equation