Eq. \ref{eq:4718749} is an initial equation. $$v_{0, x} t = x - x_0 \label{eq:4718749}$$ Divide both sides of Eq. \ref{eq:4718749} by $$v_{0, x}$$; yields Eq. \ref{eq:8858248}. $$t = \frac{x - x_0}{v_{0, x}} \label{eq:8858248}$$ Eq. \ref{eq:5756391} is an initial equation. $$y = - \frac{1}{2} g t^2 + v_{0, y} t + y_0 \label{eq:5756391}$$ Substitute LHS of Eq. \ref{eq:8858248} into Eq. \ref{eq:5756391}; yields Eq. \ref{eq:9683207}. $$y = - \frac{1}{2} g \left( \frac{x - x_0}{v_{0, x}} \right)^2 + v_{0, y} \frac{x - x_0}{v_{0, x}} + y_0 \label{eq:9683207}$$ Eq. \ref{eq:9683207} is one of the final equations. expression is a second order polynomial; projecticle motion is parabolic