It is now well established that a substantial fraction of all galaxy assembly occurs in intense bursts of star formation and black hole accretion, but the role of these two modes and how much they affect one another remains unclear. We thus investigate this in three complementary studies. In the first, we assemble a sample of 513 quasars identified by the Sloan Digital Sky Survey with detections by Herschel. These objects span a redshift range of 0 < z < 4, and their SEDs give a mean SFR of ~1000M☉/year. When comparing these SFRs to the intrinsic properties of the quasars, we find no clear connections between the quasars and the ongoing star formation events in their hosts. We then look for evidence of AGN feedback in broad absorption line (BAL) quasars, as such features are indicative of outflowing material. We find that high-ionization BAL quasars have indistinguishable properties to those of classical quasars. In our second study, which describes an iron low-ionization BAL quasar, SDSS J121441.42-000137.8, our results are again consistent with no feedback. Thus, it seems unlikely that feedback plays a dominant role in quenching star formation at the extreme SFRs seen in our BAL objects. We lastly study the host of an optically-bright quasar, SDSS J160705.16+355358.6, with evidence of an ongoing merger. We create the Point Spread Function (PSF) using a star that is in the same part of the field as our object, a method which is relatively unexplored. By subtracting the PSF, we are able to extract some of the host properties. We compare two PSF creation methods and find the empirical approach to be superior. Fits to the SEDs of the two galaxies are consistent with both falling on or above the main sequence of star formation. It is additionally plausible that these two galaxies could coalesce into a single massive quiescent galaxy by z ~ 2, and thus serve as progenitors to this class of galaxy that has proven challenging to our understanding of galaxy assembly. / Doctor of Philosophy / Quasars are among some of the brightest objects in the Universe and are powered by supermassive black holes that are rapidly accreting new material. The light from these distant objects can be detected across the electromagnetic spectrum, with each wavelength regime offering new insight into their properties. Further, if we look at their spectra, the features appear redshifted, i.e. they are at longer wavelengths compared to the expected values on Earth. More distant objects have higher redshifts. This, coupled with the constant speed of light, tells us that light from a quasar that has reached us on Earth must have been emitted many years ago; in other words, quasars offer glimpses into the past and can be used study how our Universe has assembled over time. Star formation and quasar activity in galaxies have been shown to coexist across all redshifts. This suggests a deep connection between a galaxy's stellar and black hole mass assemblies. Both peak at z ~ 2, implying that a substantial amount of all galaxy assembly took place in high-redshift, dusty bursts of star formation and quasar activity. This dust absorbs light originally emitted at optical/UV wavelengths and reradiates it in the infrared, making infrared wavelengths the perfect regime in which to investigate the connection between the two processes. In this dissertation, I have focused specifically on quasars with detections at both optical and far-infrared (FIR) wavelengths to determine what effect, if any, quasars have on the galaxies in which they reside. The optical emission of these systems describes the properties of the quasars, while the FIR estimates star formation rates (SFRs) in their hosts. Many astronomers invoke something called feedback, in which the quasar regulates the host star formation, to align theory with observations. We search for evidence of this process in the very bright quasars located within extremely star-forming systems. We, however, find no such evidence. This could imply that, at the high luminosities of our systems, feedback is not the dominant effect in regulating star formation, but perhaps some host self-regulation is instead. It could also imply that the feedback timescale is much shorter than that of either quasar or extreme star formation activity, making direct observations of feedback difficult.

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