Question

For the given graph of the quadratic polynomial $y=a{x}^2+bx+c$ as shown below. Select the correct options.

• A. $a>0$
• B. $b>0$
• C. $b^2-4ac>0$
• D. $c<0$

Answer 1

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

$c<0$

The graph of the quadratic polynomial $y=a{x}^2+bx+c$ is given as:
The graph is an upward opening parabola $\Rightarrow a>0.$
Also, the graph is cutting the $x-$ axis at two separate points
$\therefore D>0\Rightarrow b^2-4ac>0$

The vertex lies in the 4th quadrant,
Thus, the $x-$ coordinate of the vertex should be positive.
$\Rightarrow -\frac{b}{2a}>0\because a>0\Rightarrow b<0.$

Now, one root is positive, while other is negative.
$\Rightarrow \text{Product of Roots}=\frac{c}{a}<0\Rightarrow c<0$