Problem $1(25$ points$).$ A crest vertical curve is to be constructed by joining an initial tangent of

$+5\%$ with a final tangent of $-3\%.$ The station location of PVC is $10+00$ and elevation of PVC is

$600$ ft $.$ The length of the curve is $1000$ ft $.$ Determine the following:

$($a$)$ Equation of the curve $($coefficients of the parabola$).$

$($b$)$ The station location and elevation of the highest point on the curve.Problem $1(25$ points$).$ A crest vertical curve is to be constructed by joining an initial tangent of

$+5\%$ with a final tangent of $-3\%.$ The station location of PVC is $10+00$ and elevation of PVC is

$600$ ft $.$ The length of the curve is $1000$ ft $.$ Determine the following:

$($a$)$ Equation of the curve $($coefficients of the parabola$).$

$($b$)$ The station location and elevation of the highest point on the curve.