How can we tell if an ion is amphiprotic
To be amphiprotic means that the chemical species can donate or accept H+ ions. 

$$\ce{H2CO3&lt;=&gt;[H+] HCO3^- &lt;=&gt;[OH-] CO3^{2-}}$$
$$\ce{H3PO4 &lt;=&gt;[H+] H2PO4^- &lt;=&gt;[OH-] HPO4^{2-}}$$
$$\ce{CH3COOH &lt;=&gt;[H+] CH3COO^- &lt;=&gt;[OH-] \text{No Change}}$$

Thus since the acetate anion can't donate a proton, it is not amphiprotic.