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. $\frac{b}{a}>0$
• B. $abc>0$
• C. $\frac{ab}{c}<0$
• D. $\frac{bc}{a}<0$

Answer 1

Answer: (C), (D)

The correct options are
C $\frac{ab}{c}<0$
D $\frac{bc}{a}<0$


From the given graph,
$a>0$
The $x-$ coordinate of vertex is positive, so
$-\frac{b}{2a}>0\Rightarrow \frac{b}{a}<0\therefore b<0f\left(0\right)>0\Rightarrow c>0\therefore a>0,b<0,c>0$

Now, checking the options, we get
$\frac{b}{a}<0abc<0\frac{ab}{c}<0\frac{bc}{a}<0$