I am designing a rollercoaster want to seamlessly connect a known parabola to an unknown sine wave (using derivatives). The equations are:

F(x): -0.02e^1.75(x-60)^{2 +} 8.5e^1.75 - 0.027

g(x) = a(bx-c)+k

They also intersect at the point (75, 4e^1.75 -0.027)

I chose values for b and c, to find the unknown value (b= 0.1; and c=-0.73), but I was unable to separate the "a" and the "k" value. How would I find the unknown values?