Question

Suppose that you were to try to find a parabola y = ax2 + bx + c that passes through the (x, y) pairs (-5,12), (-4,-2), and (-2,5). To obtain the coefficients a, b, and c you would try to solve a system of linear equations whose augmented matrix is which?

Answer 1

Your matrix

	X1	X2	X3	b
1	25	-5	1	12
2	16	-4	1	-2
3	4	-2	1	5

Make the pivot in the 1st column by dividing the 1st row by 25

	X1	X2	X3	b
1	1	-1/5	1/25	12/25
2	16	-4	1	-2
3	4	-2	1	5

Eliminate the 1st column

	X1	X2	X3	b
1	1	-1/5	1/25	12/25
2	0	-4/5	9/25	-242/25
3	0	-6/5	21/25	77/25

Make the pivot in the 2nd column by dividing the 2nd row by -4/5

	X1	X2	X3	b
1	1	-1/5	1/25	12/25
2	0	1	-9/20	121/10
3	0	-6/5	21/25	77/25

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	-1/20	29/10
2	0	1	-9/20	121/10
3	0	0	3/10	88/5

Make the pivot in the 3rd column by dividing the 3rd row by 3/10

	X1	X2	X3	b
1	1	0	-1/20	29/10
2	0	1	-9/20	121/10
3	0	0	1	176/3

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	35/6
2	0	1	0	77/2
3	0	0	1	176/3

Solution set:

a = 35/6

b = 77/2

c = 176/3