Question

Find the sign of a, b and c in the below graph of polynomial $f\left(x\right)=a{x}^2+b$.

• A.
  $a>0,b<0andc>0$
• B.
  $a>0,b>0andc>0$
• C.
  $a<0,b<0andc>0$
• D.
  $a>0,b>0andc<0$

Answer 1

The correct option is B

$a>0,b>0andc>0$
The graph f(x) is opening upwards.
So, a >0.

As the vertex lies in third quadrant,
$\Rightarrow x<0$
$\Rightarrow \frac{-b}{2a}<0$ [ a>0 ]
Hence, b >0
As the parabola is cutting positive y-axis, c >0.
So, option b is correct.