Find a, b, and c such that the parabola y=ax^2+bx+c passes trhought the points (1,-4), (-1,0), and (2,3).
2007-09-26 07:57:45 · 2 answers · asked by rong_xu 1 in Science & Mathematics ➔ Mathematics
So plug in the given values for the given (x, y) coordinates to get three equations in a, b, and c. Then proceed to solve them just like you would any other system of 3 simultaneous linear equations.
Doug
2007-09-26 08:05:53 · answer #1 · answered by doug_donaghue 7 · 1⤊ 0⤋
The point (1, -4) satisfies the equation, so -4 = a(1)^2 + b*1 + c, or a + b + c = -4. Also, (2, 3) satisfies, so 3 = a(2)^2 + b(2) + c, or 4a + 2b + c = 3, and similarly for the point (-1, 0). This gives rise to a system:
a + b + c = -4
a - b + c = -1
4a + 2b + c = 3
...which, in turn, give rise to a matrix that can represent the system:
[[1 1 1 -4]
[1 -1 1 -1]
[4 2 1 3]]
Reduce this matrix to echelon form to solve the system, and contact me through IM or e-mail if you have more questions.
2007-09-26 15:08:25 · answer #2 · answered by Anonymous · 0⤊ 0⤋