Question:
If the graph of quadratic polynomial $a x^{2}+b x+c$ cuts negative direction of $y$-axis, then what is the sign of $c$ ?
Solution:
Since graph of quadratic polynomial $f(x)=a x^{2}+b x+c$ cuts negative direction of $y$-axis
So put $x=0$ to find the intersection point on $y$-axis
$y=0+0+c=c$
So the point is $(0, c)$
Now it is given that the quadratic polynomial cuts negative direction of $y$
So $c<0$