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Part 1 - Fitting 3 points to a quadratic equation

Enter three points:

Remember, standard form is: y = ax² + bx + c

For each point above, we substitute the x and y values to get these three equations:

y = a(x²) + b(x) + c xa + xb + 1c = y

y = a(x²) + b(x) + c xa + xb + 1c = y

y = a(x²) + b(x) + c xa + xb + 1c = y

Now we use these equation's coefficients to create a 3x3 matrix

[A]	[B]	[C]
[D]	[E]	[F]
[G]	[H]	[I]

Next, we solve this matrix for the determinant:

Det = ( ( A * E * I) + ( B * F * G) + ( C * D * H) ) - ( ( A * F * H) + ( B * D * I) + ( C * E * G) )

Det = ( ( A * E * I) + ( B * F * G) + ( C * D * H) ) - ( ( A * F * H) + ( B * D * I) + ( C * E * G) )

Det = ( ( A * E * I) + ( B * F * G) + ( C * D * H) ) - ( ( A * F * H) + ( B * D * I) + ( C * E * G) )

Next, we create the matrix that allows us to find the "a" coefficient.
For this, we replace the first column of the matrix above with the "y" values:

[Y1]	[B]	[C]
[Y2]	[E]	[F]
[Y3]	[H]	[I]

Solving this matrix for the determinate gives us:
(we won't do all the steps, use the model above!)

Det_a = Det_a

Likewise:

Det_b = Det_b

and:

Det_c = Det_c

To find the coefficients for our final equation:

Coefficient a = Det_a / Det =

Coefficient b = Det_b / Det =

Coefficient c = Det_c / Det =

So the final quadratic equation looks like:

y = ax² + bx + c