# How do you write  f(x)=x^2+2x in vertex form?

${\left(x + 1\right)}^{2} - 1$
$f \left(x\right) = {x}^{2} + 2 x$
expanding this with $+ 1 - 1$ gives:
$f \left(x\right) = {x}^{2} + 2 x + 1 - 1$ which is equivalent to $f \left(x\right) = {x}^{2} + 2 \cdot 1 \cdot x + {1}^{2} - 1$
$f \left(x\right) = {\left(x + 1\right)}^{2} - 1$