Set Fits
write a quadratic equation that fits each set of points ?
1.) (0,-8), (2,0), and (-3,-5)
2.) (-2,6), (0,-6), and (3,-9)
3.) (1,4),(-2,13), and (0,3)
Thanks 
Greetings,
Let the form of the quadratic be f(x) = ax^2 + bx + c
1) f(0) = -8 = c
f(2) = 0 = 4a + 2b + c
f(-3) = -5 = 9a - 3b + c
c = -8
4a + 2b - 8 = 0, b = 4 - 2a
9a - 3b - 8 = 0
9a - 3(4 - 2a) - 8 = 0
9a - 12 + 6a - 8 = 0
15a = 20
a = 5/4
b = 4 - 5/2 = 3/2
f(x) = (5/4)x^2 + (3/2)x - 8
2) f(-2) = 6 = 4a - 2b + c
f(0) = -6 = c
f(3) = -9 = 9a + 3b - 6
4a - 2b - 6 = 6, b = 2a - 6
9a + 3(2a - 6) - 6 = -9
15a - 18 = -3
15a = 21
a = 7/5
b = 14/5 - 6 = -16/5
f(x) = (7/5)x^2 - (16/5)x - 6
3) f(1) = 4 = a + b + c
f(-2) = 13 = 4a - 2b + c
f(0) = 3 = c
a + b + 3 = 4, a = 1 - b
4a - 2b + 3 = 13
4(1 - b) - 2b = 10
4 - 4b - 2b = 10
-6b = 6
b = -1
a = 1 + 1 = 2
f(x) = 2x^2 - x + 3
Regards
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