Parabolas intersecting in integer points

Question

Can you construct an example of two different parabolas (with integer coefficients) that intersect at three integer points?

An integer point is a point $(x,y)$ where both $x$ and $y$ are integers.

Answer 1

Example:

$$\begin{cases} x^2+4xy+4y^2-4x-5y=0,\\ 4x^2+4xy+y^2-4x-5y=0. \end{cases}$$

Courtesy of Wolfram Alpha:

I hope this helps ;-)