Parabolic Equation Calculation

Http://community.csdn.net/Expert/topic/3756/3756475.xml? Temp =. 3623011.
The coordinates (x1, Y1), (X2, Y2) of the two points on the parabolic curve are known (and the two points are measured at the two points of the parabolic curve respectively), and the Y coordinate K of the vertex, and the parabolic opening is up, that is, a> 0.

The formula is as follows: Values of A, B, and C in Y = A * x ^ 2 + B * x + C, and X coordinate H of the vertex.

This problem can be solved in this way
Assume that the equation is in the form
Y = a (x-B) ^ 2 + k
This ensures that the minimum point is the minimum value when K, x = B.
Y1-k = a (x1-b) ^ 2
A y2-k = a (x2-b} ^ 2
Based on the assumption of the owner
Obviously, Y1 and Y2 are larger than K, otherwise there will be no answer
This means that SQRT (y1-k)/(y2-k) must be valid data

Divide the root number and obtain two equations.
SQRT (y1-k)/(y2-k) = x1-b/x2-b
SQRT (y1-k)/(y2-k) =-(x1-b/x2-b)
Only the latter is valid, because the correct answer B is located between X1 and X2
So we can solve B, and then we can solve.
Then, set y = a (x-B) ^ 2 + K.
Expand to Y = AX ^ 2 + bx + c
To obtain the values of A, B, and C.

The complete calculation is

M = SQRT (y1-k)/(y2-k ))
B = (X1 + x2 * m)/(m + 1)
A = (y1-k)/(x1-b) * (x1-b ))

A =;
B = 2 * a * B
C = K + B * B
Vertex coordinates (B, K)
Parabolic equation Y = A * x ^ 2 + B * x + c