How do you explain the amphoteric behaviour of amino acids?

In aqueous solution,the carboxyl group of an amino acid can lose a proton and the amino group can accept a proton to give a dipolar ion known as a zwitter ion.
$R-CH(NH_2)-COOH \leftrightarrow R-CH(NH_3^+)-COO^-$ (Zwitter ion)
Therefore,in zwitter ionic form,the amino acid can act both as an acid and as a base.
$R-CH(NH_2)-COOH \xrightarrow{H^+} R-CH(NH_3^+)-COOH$ (Acidic medium)
$R-CH(NH_3^+)-COO^- \xrightarrow{OH^-} R-CH(NH_2)-COO^-$ (Basic medium)
Thus,amino acids show amphoteric behaviour.