Question

If graph of $y=a{x}^2-bx+c$ is following, then sign of $a,b,c$ are

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

Answer 1

The correct option is A $a<0,b<0,c<0$

$y=f\left(x\right)=a{x}^2-bx+c$
We have, $f\left(0\right)<0$
$f\left(0\right)=a(0{)}^2-b(0)+c<0$
$\Rightarrow f\left(0\right)=c<0$
And also the parabola is downward opening parabola, therefore $a<0$

We know, vertex $=\frac{-\left(b\right)}{2a}$
We have vertex $>0$
$\Rightarrow -\frac{-b}{2a}>0\Rightarrow \frac{b}{a}>0\Rightarrow b<0$