Question

Find the range of each of the following functions $f\left(x\right)=x^2-6x+11$, all $x\in R$.

Answer 1

The min value of the quadratic equation is at $x=\frac{-b}{a}$

So $x=\frac{-(-6)}{1}=6$

$f\left(6\right)=6^2-6\left(6\right)+11=11$

So the range of function is $[6,\infty )$