# How we can limit quadratic function?

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.

• Think about the roots of $f$. – Rodrigo Dias Nov 10 '16 at 13:04
• I was think about roots , but it leads to several conditions . And I want simply way to solve this . – S.H.W Nov 10 '16 at 13:07
• And I also search for a new solution. – S.H.W Nov 10 '16 at 13:08
• Unfortunately, it does have several conditions. – Rodrigo Dias Nov 10 '16 at 13:08
• But for first quadrant , it works. – S.H.W Nov 10 '16 at 13:09