R(x)= { ax^2, from A to B

{ bx+c, from B to C

B is 1000 feet horizontally from A and 100 feet higher. Since the road is smooth, R'(x) is continuous. What is the value of b?

I assume R(x) is the road height. At x = 1000 ft,

a x^2 = a*10^6 = 100, so a = 10^-4
b*1000 + c = 100
Since the slope is also continuous at x = 1000,
2x = 2*1000 = b
b = 5*10^-4

Solve for c.