C$.$ A parabolic vertical curve connects a $\backslash (+4\mathrm{.}8\backslash \%\backslash )$ grade with a $\backslash (-4\backslash \%\backslash )$ grade on a rural highway at station $\backslash (880+25\mathrm{.}4\backslash )$ and elevation $512\mathrm{.}6$ ft above the sea level. The length of the curve is $560$ ft $.$ Calculate:

i$.$ The location and elevation of the point of vertical curvature $($PVC$)$ and the point of vertical tangency $($PVT$)$

$(6$ marks$)$

ii$.$ Elevation at stations $875+50$ and $881+50$

$(4$ marks$)$