SOLUTION: A parabola with equation y=x^2+bx+c passes through the points (2,3) and (4,3). What is c?
(A)2 (B)5 (C)7 (D)10 (E)11
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-> SOLUTION: A parabola with equation y=x^2+bx+c passes through the points (2,3) and (4,3). What is c?
(A)2 (B)5 (C)7 (D)10 (E)11
(from AMC 10
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Question 263155: A parabola with equation y=x^2+bx+c passes through the points (2,3) and (4,3). What is c?
(A)2 (B)5 (C)7 (D)10 (E)11
(from AMC 10 2006 A). I'm in 7th grade and i need to study for the upcoming AMC 10 2010 Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! step 1 - plug in the coordinates to get 2 equations as
(i) 3 = 4 + 2b + c
(ii) 3 = 16 + 4b + c
now take (ii) - (i) to get
(iii) 0 = 12 + 2b
so,
b = -6
substitute this back into (i) to get
(iv) 3 = 4 + (-6)2 + c
c = 11
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