Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a],[c]}$$
We can use any software calculator to draw these two functions, as shown below.
See the graphs below.
$$\color{blue}{\bf [b]}$$
We know that
$$\Delta V=V_f-V_i=-\int_i^fE_xdx$$
where $E_x=5000 x$,
$$\Delta V =-5000\int_{x_i}^{x_f}x dx =\dfrac{-5000}{2}x^2\bigg|_{x_i}^{x_f}$$
$$\Delta V =-2500(x_f^2-x_i^2)$$
At $x_i=0$, $V_i=0$,
$$\Delta V =-2500(x_f^2-0^2)$$
replacing $x_f$ by $x$,
$$\boxed{\Delta V =-2500x^2 }$$
