Question:
If graph of quadratic polynomial $a x^{2}+b x+c$ cuts positive direction of $y$-axis, then what is the sign of $c$ ?
Solution:
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 $c>0$