Question

r(x)={0.8x, for -50<=x<=0
a x^2+b x+c , for 0<=x<=100
-1.6x+200, 100<=x<=150} ,
the quadratic function intersect 0.8x at the origin and -1.6+200 at (100,40) , find a, b,c (hint, slope of the parobola)

Answer 1

You can fit an infinite number of parabolas to two point. Do you have anything else than your two intersections?

Answer 2

The problem is about designing a roller coaster and 0.8x is the first section, parobola the second and -1.6x+200 the thrid

Answer 3

Suppose the horizontal distance at the transistion points P and Q is 100 ft. Let P be located at the origin (Hints: At each of x=0 and x=100, there are two conditions given by: i) the point on the curve and ii) the slope of the curve.

Answer 4

Then you have four conditions. f(x)=0.8x, g(x)=ax^2+bx+c, h(x)=-1.6x+200
Conditions:
1) f(0)=g(0),
2) f'(0)=g'(0),
3) g(100)=h(100),
4) g'(100)=h'(100)

From 1) you get c=0, from 2) you get b=0.8, from 3) a=-4/1000 and you can verify using 4)

Answer 5

Unfortunately 4) does not seems to verify 3) the derivative of the parobola is 2ax+b, and choose a = -4/1000 and b= 0.8, 2a*100=b does not equal to -1.6 it is 0 :(

Answer 6

True. My bad.
Well, then you problem is ill defined. Are you sure about your intersections?