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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.

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

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