If graph of quadratic polynomial ax2 + bx + c cuts positive direction of y-axis,

If graph of quadratic polynomial $f(x)=a x^{2}+b x+c$ cuts positive direction of $y$-axis, then

Put $x=0$ for the point of intersection of the polynomial and $y$-axis

We have $y=0+0+c=c$

Since the point $(0, c)$ is above the $x$-axis

Hence, the sign of $c$ is positive, that is $c>0$