The injection physics in a shock-induced density down-ramp injector was characterized, demonstrating precise control of a laser-plasma accelerator (LPA). Using a jet-blade assembly, experiments systematically varied the shock injector profile, including shock angle, shock position, up-ramp width, and acceleration length. Our work demonstrates that beam energy, energy spread, and pointing can be controlled by adjusting these parameters. As a result, an electron beam that was highly tunable from 25 to 300 MeV with 8% energy spread (ΔEFWHM/E), 1.5 mrad divergence, and 0.35 mrad pointing fluctuation was produced. Particle-in-cell simulation characterized how variation in the shock angle and up-ramp width impacted the injection process. This highly controllable LPA represents a suitable, compact electron beam source for LPA applications such as Thomson sources and free-electron lasers.