Question

The vertex of the quadratic curve $y=a{x}^2+bx+c$ lies in the fourth quadrant, if

• A. $a{x}^2+bx+c<0\forall X\epsilon R$ and $b>0$
• B. $a{x}^2+bx+c<0\forall X\epsilon R$ and $b<0$
• C. $a{x}^2+bx+c<0$ for some $x,a>0$ and $b>0$
• D. $a{x}^2+bx+c<0$ for some $x,a<0$ and $b<0$

Answer 1

The correct option is A $a{x}^2+bx+c<0\forall X\epsilon R$ and $b>0$

For x taking real values, vertex of the parabola lies in fourth quadrant if a<0, i.e, parobola should be downward parabola

See the above diagram for better understanding

In fourth quadrant $x>0$ and $y<0$

$\Rightarrow \frac{-b}{2a}>0$

As $a<0$ $\to$ $b>0$