Question

For the given graph of $y=a{x}^2+bx+c$ as shown, select the correct statements.

• A. $y>0\forall x\in (-\infty ,\alpha )\cup (\beta ,\infty )$
• B. $D>0$
• C. $a>0$
• D. $y<0\forall x\in (\alpha ,\beta )$

Answer 1

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

$y<0\forall x\in (\alpha ,\beta )$

Given the graph of $y=a{x}^2+bx+c$ as shown:

Now, from the graph, we can observe the graph is an upward opening parabola $\Rightarrow a>0$
Also, the graph cuts the $x-$ axis at two distinct points. $\Rightarrow D>0$

Also, as observed from the graph:
$y>0\forall x\in (-\infty ,\alpha )\cup (\beta ,\infty )\&y<0\forall x\in (\alpha ,\beta ).$