Given the 3 points you entered of (1,1), (2,3), and (4,5):
Calculate the quadratic equation formed by those 3 points
b = x-coordinate of 1
a = x-coordinate squared
12 = 1
c is always equal to 1
d = our y-coordinate of 1
f = x-coordinate of 2
e = x-coordinate squared
22 = 4
g is always equal to 1
h = our y-coordinate of 3
j = x-coordinate of 4
i = x-coordinate squared
42 = 16
k is always equal to 1
l = our y-coordinate of 5
Δ = (a * f * k) + (b * g * i) + (c * e * j) - (c * f * i) - (a * g * j) - (b * e * k)
Δ = (1 * 2 * 1) + (1 * 1 * 16) + (1 * 4 * 4) - (1 * 2 * 16) - (1 * 1 * 4) - (1 * 4 * 1)
Δ = 2 + 16 + 16 - 32 - 4 - 4
Δ = -6
a numerator = (d * f * k) + (b * g * l) + (c * h * j) - (c * f * l) - (d * g * j) - (b * h * k)
a numerator = (1 * 2 * 1) + (1 * 1 * 5) + (1 * 3 * 4) - (1 * 2 * 5) - (1 * 1 * 4) - (1 * 3 * 1)
a numerator = 2 + 5 + 12 - 10 - 4 - 3
a numerator = 2
b numerator = (a * h * k) + (d * g * i) + (c * e * l) - (c * h * i) - (a * g * l) - (d * e * k)
b numerator = (1 * 3 * 1) + (1 * 1 * 16) + (1 * 4 * 5) - (1 * 3 * 16) - (1 * 1 * 5) - (1 * 4 * 1)
b numerator = 3 + 16 + 20 - 48 - 5 - 4
b numerator = -18
c numerator = (a * f * l) + (b * h * i) + (d * e * j) - (d * f * i) - (a * h * j) - (b * e * l)
c numerator = (1 * 2 * 5) + (1 * 3 * 16) + (1 * 4 * 4) - (1 * 2 * 16) - (1 * 3 * 4) - (1 * 4 * 5)
c numerator = 10 + 48 + 16 - 32 - 12 - 20
c numerator = 10
a = | a numerator |
Δ |
a = | 2 |
-6 |
a = -0.33333333333333
b = | b numerator |
Δ |
b = | -18 |
-6 |
b = 3
c = | c numerator |
Δ |
c = | 10 |
-6 |
c = -1.6666666666667