Question 831559: parabola equation through (1,-2) (2,-4) (3,-4)in y=ax^2+bx+c
(1,1) (-1,-3) (-3,1)
(-2,9) (-4,5) (1,0)
(-1,17) (1,17) (2,8)
determine if quadratic model exsist if so then write a model
f(-2)=16 f(0)=0 f(1)=4
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
I will do the first one, you do the others using the same method:
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y = ax^2 + bx + c
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given:
(1,-2) (2,-4) (3,-4)
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(1,-2):
-2 = a + b + c
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(2,-4):
-4 = 4a + 2b + c
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(3,-4):
-4 = 9a + 3b + c
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linear system:
-2 = a + b + c
-4 = 4a + 2b + c
-4 = 9a + 3b + c
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put the system of linear equations into standard form:
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x = a
y = b
z = c
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-2 = x + y + z
-4 = 4x + 2y + z
-4 = 9x + 3y + z
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x + y + z = -2
4x + 2y + z = -4
9x + 3y + z = -4
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x = a = 1
y = b = -5
z = c = 2
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y = ax^2 + bx + c
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solution:
y = x^2 - 5x + 2
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