Competitive Inhibition - inhibitor binds to active site and competes with substrate, this can be overcome by increasing substrate concentration. So, since Km = substrate concentration to reach vmax/2, km should increase and since the effects of this inhibitor can be overcome, vmax does not change
Non competitive Inhibitor - inhibitor binds to the allosteric site and change conformation of the enzyme. So, we can't overcome the effects by increasing substrate concentration and Km should not change. By altering the enzymes, vmax decreases
Uncompetitive Inhibitors - inhibitor binds to ES complex and increases the affinity of the complex so the substrate can't be converted to product or leave the enzyme. An increase in affinity means a decrease in Km, and since it is making some of the enzyme molecules unavailable for future reactions with the substrate, vmax decreases.
Mixed Inhibition - here the inhibitor can bind either to enzyme or ES complex. If it binds to enzyme, it can making the enzyme molecules unavailable for future reactions and so vmax decreases, and making the enzyme not bind to substrate i.e. less affinity for the substrate means km increases. If the inhibitor binds to the ES complex, it is increasing the affinity of the ES and km decreases and because the enzyme is now no longer available for future reactions, vmax decreases.