SOLUTION: Find the equation of the parabola that passes through the following points.
(0,-12), (6,12), (2,-8)
Algebra.Com
Question 828351: Find the equation of the parabola that passes through the following points.
(0,-12), (6,12), (2,-8)
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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y = ax^2 + bx + c
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(0,-12)
-12 = c
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(6,12)
12 = a36 + b6 + c
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(2,-8)
-8 = a4 + b2 + c
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the linear system:
-12 = c
12 = a36 + b6 + c
-8 = a4 + b2 + c
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put the system of linear equations into standard form:
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x = a
y = b
z = c
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-12 = z
12 = 36x + 6y + z
-8 = 4x + 2y + z
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z = -12
36x + 6y + z = 12
4x + 2y + z = -8
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = a = 0.5
y = b = 1
z = c = -12
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system matrix
0 0 1
36 6 1
4 2 1
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inverse of system matrix
0.083333333 0.041666667 -0.125
-0.66666667 -0.083333333 0.75
1 0 0
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determinant of system matrix = 48
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answer:
y = 0.5x^2 + x - 12
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Solve and graph linear equations:
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---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
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