Initial velocity $\mathrm{= }\overrightarrow{\text{u}}$

$\overrightarrow{\text{u}}={\text{u}}_{\text{x}}\overrightarrow{\text{i}}\text{\&}{\text{u}}_{\text{y}}\overrightarrow{\text{j}}=\overrightarrow{\text{i}}+\overrightarrow{2\text{j}}$

Where $u_x$ = velocity along ground

$u_y$ = velocity along vertical direction

at time t, let (x, y) be the coordinates of the projectile

$x=u_{x}t$    so   $t=\frac{x}{u_x}$

But $u_x=1$ and $u_y=2$

$t=\frac{x}{1}=x$

$y=u_{y}t-\left(\frac{1}{2}g{t}^2\right)$

$y=2x-\left(\frac{1}{2}\right)\times 10x^2$

$y=2x-5x^2$ is the equation of the trajectory.