Using two kinematics equations, which are the parametric equations, a uniform linear motion in horizontal direction and a non-uniform linear motion in vertical directions, a parabolic trajectory can be obtained.
horizontal direction Link to heading
In $x$ direction ..
$$\tag{1} $$
..
vertical direction Link to heading
In $y$ direction ..
$$\tag{2} $$
..
combining equations Link to heading
Using previous equations ..
$$\tag{3} $$
..