Consider quadratic function : $f(x) = Ax^2 + Bx + C$
We Want to obtain $A$ , $B$ and $C$ by inequalities to $f(x)$ passes the first quadrant of Cartesian coordinate or Second or third or fourth.
How we can obtain range of these coefficients ?
Note : I find an equality to $f(x)$ pass the first quadrant . We know in first quadrant $x > 0$ and $y>0$ . So , we have $A + B + C > 0$ . But I couldn't use this for other quadrants.