Give a coordinate paper, just use $8 \times 8$ squares($9 \times 9$ lines), we call the crossing of lines are int-points.
Now draw a parabola, how it can pass the most int-points?
I know, when the style is $f(x)=ax^2+bx+c$, the $f(x)=\frac{x^2}{2}+\frac{x}{2}+1$ can pass $8$ int-points, it is the most. but if rotation the parabola, how to do it?