A $-4\mathrm{.}25\%$ grade intersects a $+3\mathrm{.}00\%$ grade at station $43+00$ where the elevation is $497\mathrm{.}53$ ft $.$ An equal$-$tangent vertical parabolic curve $900$ ft $.$ long has been selected to join the two tangents.

$5$ pts a$)$ Determine the stations and elevations of the BVC $($or PVC$)$ and the EVC $($or PVT$).$ Express the elevation to the nearest hundredth $(2$ decimals$).$

$5$ pts b$)$ Compute the elevation at station $42+00.$ Express your answer to the nearest hundredths $(2$ decimals$).$

$5pts$ c$)$ Determine the station and elevation of the lowest point on the curve. Express the elevation to the nearest hundredths $(2$ decimals$).$