Question

The range of the expression $f\left(x\right)=3x^2-12x+5$ is

• A. $[-7,\infty )$
• B. None of these
• C. $[-4,\infty )$
• D. $(-\infty ,-4]$

Answer 1

The correct option is A

$[-7,\infty )$

Compare $3x^2-12x+5$ with $a{x}^2-bx+c$

Here, $a>0$ $\Rightarrow$ Minimum value of $f\left(x\right)$ occur at $x=\frac{-b}{2a}$ and the value is $\frac{-D}{4a}$

$D=b^2-4ac$

$={\left(12\right)}^2-4\left(3\right)\left(5\right)=84$

Minimum value $=\frac{-84}{12}=-7$

As $a>0$, graph of $f\left(x\right)$ is upward:

Minimum value is $-7$,

Maximum value extends to $\infty$

So, the range is $[-7,\infty$)