Finding the equation of two parabolas using differentiation

[thestormbreaker]

I need help in finding the equations of two parabola's. One has a turning point at (60,10). The second crosses through the origin (0,0). They both need to join smoothly and have the points (24,5). Differentiation needs to be used to ensure that the gradient of the curve meet smoothly. The graph look something like this to give you the whole picture. The graph needs to be considered as two parabolas.

http://img468.imageshack.us/img468/8946/graphwl8.th.png

Here is my working on how I got the equation to one of the parabolas. But I am not sure what to do next.

http://img518.imageshack.us/img518/3370/equation1tc0.png

Is anyone able to help me please. Try and show the basic steps of how you came to solve it.

Thanks

 

[Dick]

A general form for a parabola passing through the origin is e.g. y=x*(b*x+c). (Just take the more general form y=b*(x-c)^2+d and put x=0, y=0 and see what that means in terms of the coefficients). Now put in the conditions y=5 when x=24 and set y'=2*b*x-c equal to the derivative of the other parabola at (24,5). Two equations in two unknowns.