Question

Find the range of the following functions:
$f\left(x\right)=x^2+2x+3$

Answer 1

$f\left(x\right)=x^2+2x+3=(x+1{)}^2+4$

So, $Min\left(f\right(x\left)\right)=4$

At $x=-1$

And $Max\left(f\right(x\left)\right)=\infty$

Thus range$⟹(4,\infty )$