Given the 3 points you entered of (1,1), (2,3), and (4,5), calculate the quadratic equation formed by those 3 points

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Given the 3 points you entered of (1,1), (2,3), and (4,5):

Calculate the quadratic equation formed by those 3 points

Use Cramers Rule

b = x-coordinate of 1

a = x-coordinate squared
1² = 1

c is always equal to 1

d = our y-coordinate of 1

Determine values (e, f, g, h)

f = x-coordinate of 2

e = x-coordinate squared
2² = 4

g is always equal to 1

h = our y-coordinate of 3

Determine values (i, j, k, l)

j = x-coordinate of 4

i = x-coordinate squared
4² = 16

k is always equal to 1

l = our y-coordinate of 5

Calculate Delta (Δ):

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

Calculate the a numerator:

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

Calculate the b numerator:

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

Calculate the c numerator:

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

Calculate a

a = -0.33333333333333

Calculate b

b = 3

Calculate c

c = -1.6666666666667

Build our quadratic equation:

You have 2 free calculationss remaining

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Tags:

• 3 point equation
• equation
• point
• quadratic