Question

The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below


Which of the following options is/are true for the graph?

• A. $a-b+c>0$
• B. $4a-2b+c<0$
• C. $9a-3b+c>0$
• D. $a-2b+4c<0$

Answer 1

Answer: (A), (C)

The correct options are
A $a-b+c>0$
C $9a-3b+c>0$


From the given graph,
$f\left(x\right)>0,\forall x\in R$
Now,
$f(-1)>0\Rightarrow a-b+c>0$

Similarly,
$f(-2)>0\Rightarrow 4a-2b+c>0f(-3)>0\Rightarrow 9a-3b+c>0f(-\frac{1}{2})>0\Rightarrow \frac{a}{4}-\frac{b}{2}+c>0\Rightarrow a-2b+4c>0$