SOLUTION: Given the equation: Ax2 + Bx + C. When y is equal to 41, x is equal to -2. When y is equal to 20, x is equal to 5. When minimized, x is equal to 2. Find the sum of A and B.

Question 1179261: Given the equation: Ax2 + Bx + C. When y is equal to 41, x is equal to -2. When y is
equal to 20, x is equal to 5. When minimized, x is equal to 2. Find the sum of A and B.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
y = Ax^2 + Bx + C
41 = A(-2)^2 + B(-2) + C
20 = A(5)^2 + B(5) + C
When minimized, dy/dx = 0 = 2Ax + B -> 2(2)A + B = 0 -> B = -4A
Substitute in the 1st two equations:
41 = 4A + 8A + C -> 41 = 12A + C
20 = 25A - 20A + C -> 20 = 5A + C
Subtract the 2nd from the 1st:
21 = 7A -> A = 3
Thus B = -12, and C = 41 - 12(3) -> C = 5
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