Question

The range of the function $f\left(x\right)=x^2-6x+7$ is

• A. $[2,3]$
• B. $(-\infty ,-2)$
• C. $(-\infty ,\infty )$
• D. $[-2,\infty )$

Answer 1

The correct option is D $[-2,\infty )$

Let $y=x^2-6x+7$
$\because f\left(x\right)$ is a quadratic function
On comparing with $a{x}^2+bx+c=0$, we get
$a=1>0,b=-6,c=7$
$\therefore$ range will be $[-\frac{D}{4a},\infty )$
$=[-2,\infty )$