Surveying civil engineering

vertical parapolic curve method

Question :

$(4)$ A vertical curve is a quadratic equation: $y=a{x}^2+bx+c,$ where $y$ is the height difference between a point on the vertical curve and the starting point of the curve, and $x$ is the horizontal distance from the starting point of the vertical curve. It is known that the mileage of the previous VPI $1($VPI is the intersection point of the two slope lines$)$ is $235K+420$ and its height is $200\mathrm{.}350$ meters, while the VPI $2$ mileage of the current vertical curve is $236K+660,$ and its height is $138\mathrm{.}350$ meters as well as the VPI $3$ mileage of the next vertical curve is $237K+520,$ and its height is $164\mathrm{.}150$ meters The horizontal length of the current vertical curve is $500$ meters. Please find the downhill and uphill slopes, the equation of the current vertical curve, also calculate the height and the mileage of the beginning point, the end point, the lowest point $($or the highest point$),$ the middle point of the current vertical curve. $(25$ pts$.)$