Given the 3 points you entered of (1,2), (3,4), and (5,6):
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 2
f = x-coordinate of 3
e = x-coordinate squared
32 = 9
g is always equal to 1
h = our y-coordinate of 4
j = x-coordinate of 5
i = x-coordinate squared
52 = 25
k is always equal to 1
l = our y-coordinate of 6
Δ = (a * f * k) + (b * g * i) + (c * e * j) - (c * f * i) - (a * g * j) - (b * e * k)
Δ = (1 * 3 * 1) + (1 * 1 * 25) + (1 * 9 * 5) - (1 * 3 * 25) - (1 * 1 * 5) - (1 * 9 * 1)
Δ = 3 + 25 + 45 - 75 - 5 - 9
Δ = -16
a numerator = (d * f * k) + (b * g * l) + (c * h * j) - (c * f * l) - (d * g * j) - (b * h * k)
a numerator = (2 * 3 * 1) + (1 * 1 * 6) + (1 * 4 * 5) - (1 * 3 * 6) - (2 * 1 * 5) - (1 * 4 * 1)
a numerator = 6 + 6 + 20 - 18 - 10 - 4
a numerator = 0
b numerator = (a * h * k) + (d * g * i) + (c * e * l) - (c * h * i) - (a * g * l) - (d * e * k)
b numerator = (1 * 4 * 1) + (2 * 1 * 25) + (1 * 9 * 6) - (1 * 4 * 25) - (1 * 1 * 6) - (2 * 9 * 1)
b numerator = 4 + 50 + 54 - 100 - 6 - 18
b numerator = -16
c numerator = (a * f * l) + (b * h * i) + (d * e * j) - (d * f * i) - (a * h * j) - (b * e * l)
c numerator = (1 * 3 * 6) + (1 * 4 * 25) + (2 * 9 * 5) - (2 * 3 * 25) - (1 * 4 * 5) - (1 * 9 * 6)
c numerator = 18 + 100 + 90 - 150 - 20 - 54
c numerator = -16
a = | a numerator |
Δ |
a = | 0 |
-16 |
a = 0
b = | b numerator |
Δ |
b = | -16 |
-16 |
b = 1
c = | c numerator |
Δ |
c = | -16 |
-16 |
c = 1