Question

Use a system of equations to find the parabola of the form

y=ax^2+bx+c

that goes through the three given points.

(2,-12)(-4,-60)(-3,-37)

Answer 1

for point (2,-12)

for point (-4,-60)

for point (-3,-37)

.

from these 3 equations system Ax=b is

augmented matrix is

4	2	1	-12
16	-4	1	-60
9	-3	1	-37

convert into Reduced Row Eschelon Form...

Divide row1 by 4

1	1/2	1/4	-3
16	-4	1	-60
9	-3	1	-37

Add (-16 * row1) to row2

1	1/2	1/4	-3
0	-12	-3	-12
9	-3	1	-37

Add (-9 * row1) to row3

1	1/2	1/4	-3
0	-12	-3	-12
0	-15/2	-5/4	-10

Divide row2 by -12

1	1/2	1/4	-3
0	1	1/4	1
0	-15/2	-5/4	-10

Add (15/2 * row2) to row3

1	1/2	1/4	-3
0	1	1/4	1
0	0	5/8	-5/2

Divide row3 by 5/8

1	1/2	1/4	-3
0	1	1/4	1
0	0	1	-4

Add (-1/4 * row3) to row2

1	1/2	1/4	-3
0	1	0	2
0	0	1	-4

Add (-1/4 * row3) to row1

1	1/2	0	-2
0	1	0	2
0	0	1	-4

Add (-1/2 * row2) to row1

1	0	0	-3
0	1	0	2
0	0	1	-4

reduced system is

solution is

.