An object is moving with a uniform acceleration which is parallel...

From the equations of kinematics, ${v}^{2} - {u}^{2} = 2as$

For, initial velocity, $u = 0 ⇒ {v}^{2} = 2as$

So the graph of $s - v$ passes from origin and it will be symmetric about $s$-axis because for same value of $s$ for both negative and positive value of $v$.