a parabola with the x intercepts at (-1, 0) and (3, 0) which passes through the point (1,-8)
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y = ax^2 + bx + c is the parabola
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At (-1,0):
0 = a*(-1)^2 -b + c
a - b + c = 0 ------ Eqn 1
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At (3,0):
0 = a*9 + 3b + c
9a + 3b + c = 0 ---------- Eqn 2
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At (1,-8):
-8 = a + b + c
a + b + c = -8 ---- Eqn 3
a - b + c = 0 ------ Eqn 1
----------------------------- Subtract
2b = -8
b = -4
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0 = a*9 + 3b + c ---------- Eqn 2
9a + 3b + c = 0
9a + c = 12
a + c = -4
-------------------------- Subtract
8a = 16
a = 2
=================
a - b + c = 0 ------ Eqn 1
2 + 4 + c = 0
c = -6
=======================
2x^2 - 4x - 6 = 0 is the parabola
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Another method:
| x x^2 y 1|
|-1 1 0 1|
| 3 9 0 1| = 0
| 1 1 -8 1|
This method is easily made into an Excel sheet.