Question

If $a<0$ and $D<0$, what can be inferred about $f\left(x\right)=a{x}^2+bx+c?$

• A. $f\left(x\right)=$ is always positive
• B. $f\left(x\right)=0$ always
• C. Cannot determine nature of $f\left(x\right)$
• D. $f\left(x\right)$ is always negative

Answer 1

The correct option is D

$f\left(x\right)$ is always negative

When $a<0$,the graph of $f\left(x\right)=a{x}^2+bx+c$ will be in the shape of inverted bowl.

Also, $D<0$ indicates that $f\left(x\right)$ does not cut x-axis

So, the graph of $f\left(x\right)$ will look as

From graph, we can see that $f\left(x\right)$ is always negative