How can we tell if an ion is amphiprotic If I had the following ions:
$$\ce{HCO3^-}$$
$$\ce{H2PO4^-}$$
$$\ce{CH3COO^-}$$

Which ones would be amphiprotic?

Looking at my $ K_A$ chart, it looks like each ion is formed by the disassociation of weak acids, so It looks like all of them are amphiprotic because they could all technically act as a bronstead-lowry base.  

The answer is the first two ions, but why? 

Thanks for answering :)
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.