What do the dotted lines or partial bonds in a resonance hybrid represent?

They represent the delocalization of electrons across the bonds; therefore, the charge is shared among multiple atoms depending on the specific resonance hybrid you are looking at.

What types of bacteria/archaea would exist on the ocean floor next to hydrothermal vents?

Bacteria/Archaea that exist at that depth in extreme temperature must be extremophiles, but more specifically they would need to be barophilic to withstand the pressure and hyperthermophilic to withstand the extreme temperatures.

State the vertex and x-intercept(s) for the following equation: f(x)=x^(2)-x-20.

Vertex=(1,-20) and the x-intercepts are at x=5 and x=-4.