What's the formula given three points to come up with the quadratic equation were your give points
(x1, y1 ) (x2, y2) (x3, y3)
I remember seeing some really long equation were you just plug the numbers into it and get your answer but I have forgotten the equaiton
I think it required zeroing some things out
it had three parts i think with fraction in both of them
Well, here is a way to find a polynomial in x^n for any (n+1) points:
If you have points (X1, Y1), (X2,Y2), (X3,Y3) .... (Xn+1 , Yn+1)
then a function that goes through one of those points (Xp,Yp) and is zero at all of the others is:
Yp [ (X-X1)... (X-Xp-1)(Xp-Xp+1) ... (X-Xn+1) ] / [(Xp-X1)(Xp-X2)(Xp-Xp-1)...(Xp-Xp+1) ...(Xp-Xn+1)
note - skips (X-Xp) on top and (Xp-Xp) on bottom) for each point p so function is zero at all given points except p but is Yp at p.
Then if you add those functions you get a polynomial that goes through each point.
Now if n = 3
y= Y1[ (x-X2)(x-X3)] / [(X1-X2)(X1-X3)]
+ Y2[ (x-X1)(x-X3)] / [(X2-X1)(X2-X3)]
+ Y3[ (x-X1)(x-X2)] / [(X3-X1)(X3-X2)]
I suspect that is what you mean.
To determine the quadratic equation given three points, you can use the process of interpolation. Here's the general method:
1. Begin by assuming that the quadratic equation has the form: y = ax^2 + bx + c.
2. Substitute the coordinates of the three given points into the equation. This will give you a system of three equations:
For point 1: y1 = ax1^2 + bx1 + c
For point 2: y2 = ax2^2 + bx2 + c
For point 3: y3 = ax3^2 + bx3 + c
3. Rearrange each equation to isolate a, b, and c.
For point 1: ax1^2 + bx1 + (c - y1) = 0 (equation 1)
For point 2: ax2^2 + bx2 + (c - y2) = 0 (equation 2)
For point 3: ax3^2 + bx3 + (c - y3) = 0 (equation 3)
4. Solve this system of equations simultaneously to find the values of a, b, and c.
One approach is to use matrix algebra or Gaussian elimination to solve the system of equations. However, this can be time-consuming if done manually. Alternatively, you can use a computational tool or software, such as Wolfram Alpha or a spreadsheet program, to solve the equations numerically.
Once you have obtained the values of a, b, and c, you can substitute them back into the general quadratic equation (y = ax^2 + bx + c) to obtain the specific equation that represents the given three points.