Description
(1 pt) Suppose the graph of the equation y=A+B(x−1)+C(x−1)(x+1) contains the points (1,2) and (−1,15) in the (x,y) plane. What are the values of A and B? A= and B=
Explanation & Answer
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y = A + B(x - 1) + C(x - 1)(x +1) --- (1)
Since (1, 2) is a point on the curve it must satisfy the equation.
So, substitute x = 1 and y = 2 in equation (1)
2 = A + B(1 - 1) + C(1 - 1)(1 + 1)
2 = A + B(0) + C(0)(2)
2 = A + 0 + 0
A = 2
So, equation (1) becomes
y = 2 + B(x - 1) + C(x - 1)(x +1) --- (2)
Since (-1, 15) is also a point on the curve it must satisfy the equation.
So, substitute x = -1 and y = 15 in equation (2)
15 = 2 + B(-1 - 1) + C(-1 - 1)(-1 + 1)15 = 2 + B(-2) + C(-2)(0)
15 = 2 - 2B
15 - 2 = -2B
13 = -2B
-2B = 13
B = -13/2
So, equation (2) becomes
ANSWER: A = 2 , B =
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