1. multiple unknowns!!

Hi I am have troubles solving for a and b.

Sections 1,2 and 3 all join and are continuous. At points B and C the gradient at the end of one function is the same as the gradient at the beginning of the next.

For section 1, i.e. A to B, y=0.01x^2-1.2x+50
For section 2, i.e. B to C, y=ax^2+bx-250
For section 3, i.e. C to D, y=cx^2+dx+605

Point A is ( 0,e=50 )
Point B is ( 100,f=30)
Point C is ( 150,g )
Point D is ( h,0 )

I found e=50 and f =30.

I cant solve for the other unknowns??

2. I believe there is something wrong with the problem statement.

Consider the segments A--> B and B--> C. You state that the functions for the two segments must be equal at point B AND the derivatives of the functions must be equal at point B. Setting the derivatives equal, gives a=0.01 and b = -1.2, which does not result in the functions being equal.

3. Yes, $e= .01(0)^2- 1.2(0)+ 50= 50$ and [tex]f= .01(100)^2- 1.2(100)+ 50= 30. Also, y'= 2(.01)(100)+ 1.2= 3.2.

At point B, x= 100 so you want $y= .01(100)^2- 1.2(100)+ 50= 30= a(100)^2+ bx- 250$ and $y'= .02(100)- 1.2= 3.2= 2a(100)+ b$.
From those two equations, you can solve for a and b.

At point C, x= 150 so you want $a(150)^2+ b(150)- 250= c(150)^2+ d(150)+ 605$ and $2a(150)+ b= 2c(150+ d$.

Since you now know a and b, you should be able to solve for c and d.