Question

The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below. Then which of the following option(s) is/are correct ?

• A. $c<0$
• B. $b>0$
• C. $a+b-c>0$
• D. $abc<0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $c<0$
B $b>0$
C $a+b-c>0$
D $abc<0$


Since, graph is upward opening.
$\therefore a>0$
Graph intersects with $y-$axis in $-ve$ region.
$\therefore c<0$
Now, the vertex of the parabola is in $-ve$ side of the $x-$axis.
$\therefore -\frac{b}{2a}<0\Rightarrow b>0$

$\therefore abc<0$
$a+b>0,c<0\Rightarrow a+b>0,-c>0\therefore a+b-c>0$