Proteus mirabilis is a Gram-negative, facultatively anaerobic, rod-shaped (bacillus) bacteria. It produces large amounts of the enzyme urease, which is able to hydrolyze urea to ammonia, causing the distinctively high pH seen in the urine of individuals with a P. mirabilis infection.  

Bacteria are classified as either Gram positive or Gram negative. Gram positive bacteria stain purple because of their thick peptidoglycan cell wall. Staph and Strep groups are both Gram positive. Bacteria can then be organized based on their shape. Cocci are circular while bacilli are rectangular in shape. Staph grows in clusters.

The two most common bacterial arrangements are Staph- and Strep-. Staph- is a non-symmetrical arrangement like a cluster of grapes. Strep- indicates a chain of bacteria.

The three most common bacterial shapes are listed below.

Coccus—round or oval

Bacillus—rectangular or rod-shaped

Spirilla (spirochete)—spiral

By breaking down names into arrangement and shape, students can predict or identify the appearance of an organism by its name. In the example Staph indicates arrangement in a chain. Coccus indicates round or oval in shape. Therefore, Staphylococci are round or oval-shaped organisms arranged in a cluster.

Bordetella pertussis is a Gram negative, rod-shaped aerobe. It requires oxygen to function and commonly infects the respiratory tract of young children, causing whooping cough. 

Neisseria gonorrhoeae is a Gram negative coccus bacterium that generally presents as a diplococcus (in pairs of cocci). 

Vibrio cholerae is classified as Gram negative facultative rods. This bacteria is the most well known amongst the Vibrio species as it's the cause of cholera, which produces a toxin that causes very severe diarrhea.

Bacteria or any other microbes that feed on dead matter are termed saprophytes. Thermophilic microbes thrive in heated environments, halophiles such as Vibrio parahaemolyticus prefer salt water, and archaebacteria are a group of bacteria found in high heat, high salt content locations such as sewage treatment plants and are able to tolerate many extreme habitats.

E. coli is a Gram negative rod. It's a lactose fermenting bacteria commonly implicated in urinary tract infections and less frequently in gastroenteritis. 

Staphylococcus species are Gram positive, catalase positive cocci. The most famous member of this bacterial species, Staphylococcus aureus, is commonly implicated in skin infections, upper respiratory infections, and gastroenteritis (food poisoning).

Staphyloccocus aureus are Gram positive cocci. Chlamydia trachomatis and Rikettsia prowazekii are both classified as Gram negative rods and Neisseria meningitidis are Gram negative cocci.