Equations of the three parabolas

[jrm2002]

Homework Statement

Computing the equations of the three parabolas involved

Homework Equations

y=A1x^2 + B1

y= A2x^2+B2

y=A3x^2+B3

The Attempt at a Solution

Tried to get the constants A and B but unsuccessful!


See the attached file for the three parabolas.The dotted points indiacate the change in curvature.
How to get 2 constants in each of the three parabolas?Please help!

 

[berkeman]

Pretty hard to solve for the numbers when there are no number labels on the graphs... Am I missing something?

 

[Integral]

You will need to specify the spline points, that is, where your parabolas meet.

You should also match the slopes at those points.

Next trouble is that you have:

$$A_n x^2 + B_n$$ where n = 1,2,3
But you need:
$$A_n (x - {k_n})^2 + B_n$$ where n = 1,2,3
Where the $k_n$ specify the x coordinate of the apex of the parabola.


Matching the slopes seems to requires:
$$A_n (x_n- k_n) = A_{n+1}(x_n-k_{n+1})$$ for n = 1 2 where $x_n$ is your 2 spline points.

By matching the slopes you will avoid having a corner at the matching point.

 

[jrm2002]

The total length is 7 metres.
The first parabola meets the second at 0.7 metres.
The second parabola meets the third at 6.3 metres.

As you see,at the points where the parabolas meet, there is a change in curvature

 

[berkeman]

Not enough data. What are the x,y points of join?

 

[Integral]

The more information you can provide the easier it will be to help. Currently we are having to guess what it is you are trying to do. Could you please make an effort to actually express what it is you are trying to do. Use more then 3 words in a sentence.

Now, that said, go back and read my last post. Until you get a correct experssion for each of the parabolas there is no way you can arrive at a correct solution. The equations in your original post cannot work. They represent 3 parabolas centered at zero, if I guess correctly NONE of your parabolas have a center at zero.


If you do not want to match slopes at the splines that is your call, just means you do not have those as constraints.