The electron has an initial velocity along the x-direction $\left({\mathit{v}}_{\mathit{x}}={\mathit{v}}_0\right).$
The electric field is applied along the y-direction $\left({\mathit{E}}_{\mathit{y}}={\mathit{E}}_0\right).$
The force acting on the electron is $\overrightarrow{\mathit{F}}=-\mathit{e}\overrightarrow{\mathit{E}}=-\mathit{e}{\mathit{E}}_{\mathit{o}}\stackrel{\wedge }{\mathit{j}}$.
This produces a constant acceleration in the y-direction $\left({\mathit{a}}_{\mathit{y}}=-\frac{\mathit{e}{\mathit{E}}_0}{\mathit{m}}\right)$, while the velocity along x remains unchanged.
Since $\mathit{x}={\mathit{v}}_{\mathit{o}}\mathit{t}$ and $\mathit{y}=1\frac{2}{{\mathit{a}}_{\mathit{y}}}{\mathit{t}}^2$, eliminating time gives $\mathit{y}\propto {\mathit{x}}^2$, which represents a parabolic trajectory.
The electron follows a parabolic path.