Given the 3 points you entered of (2,2), (3,4), and (8,9):
Calculate the quadratic equation formed by those 3 points
Use Cramers Rule
b = x-coordinate of 2
a = x-coordinate squared
22 = 4
c is always equal to 1
d = our y-coordinate of 2
Determine values (e, f, g, h)
f = x-coordinate of 3
e = x-coordinate squared
32 = 9
g is always equal to 1
h = our y-coordinate of 4
Determine values (i, j, k, l)
j = x-coordinate of 8
i = x-coordinate squared
82 = 64
k is always equal to 1
l = our y-coordinate of 9
Calculate Delta (Δ):
Δ = (a * f * k) + (b * g * i) + (c * e * j) - (c * f * i) - (a * g * j) - (b * e * k)
Δ = (4 * 3 * 1) + (2 * 1 * 64) + (1 * 9 * 8) - (1 * 3 * 64) - (4 * 1 * 8) - (2 * 9 * 1)
Δ = 12 + 128 + 72 - 192 - 32 - 18
Δ = -30
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 = (2 * 3 * 1) + (2 * 1 * 9) + (1 * 4 * 8) - (1 * 3 * 9) - (2 * 1 * 8) - (2 * 4 * 1)
a numerator = 6 + 18 + 32 - 27 - 16 - 8
a numerator = 5
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 = (4 * 4 * 1) + (2 * 1 * 64) + (1 * 9 * 9) - (1 * 4 * 64) - (4 * 1 * 9) - (2 * 9 * 1)
b numerator = 16 + 128 + 81 - 256 - 36 - 18
b numerator = -85
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 = (4 * 3 * 9) + (2 * 4 * 64) + (2 * 9 * 8) - (2 * 3 * 64) - (4 * 4 * 8) - (2 * 9 * 9)
c numerator = 108 + 512 + 144 - 384 - 128 - 162
c numerator = 90
Calculate a
| a = | a numerator |
| Δ |
| a = | 5 |
| -30 |
a = -0.16666666666667
Calculate b
| b = | b numerator |
| Δ |
| b = | -85 |
| -30 |
b = 2.8333333333333
Calculate c
| c = | c numerator |
| Δ |
| c = | 90 |
| -30 |
c = -3
Build our quadratic equation:
You have 2 free calculationss remaining
How does the 3 Point Equation Calculator work?
This calculator has 3 inputs.
What 4 formulas are used for the 3 Point Equation Calculator?
a numerator = (d * f * k) + (b * g * l) + (c * h * j) - (c * f * l) - (d * g * j) - (b * h * k)
b numerator = (a * h * k) + (d * g * i) + (c * e * l) - (c * h * i) - (a * g * l) - (d * e * k)
(a * f * l) + (b * h * i) + (d * e * j) - (d * f * i) - (a * h * j) - (b * e * l)
For more math formulas, check out our Formula Dossier
What 4 concepts are covered in the 3 Point Equation Calculator?
- 3 point equation
- The equation of a parabola passing through 3 two-dimensional points
- equation
- a statement declaring two mathematical expressions are equal
- point
- an exact location in the space, and has no length, width, or thickness
- quadratic
- Polynomials with a maximum term degree as the second degree
Example calculations for the 3 Point Equation Calculator
3 Point Equation Calculator Video
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