Mathematics Tutor: None Selected Time limit: 1 Day

(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=

Jun 16th, 2015

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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

$y = 2 -\frac{13}{2}(x - 1) + C(x - 1)(x +1) --- (3)$

ANSWER:    A = 2 ,  B = $-\frac{13}{2}$

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Jun 16th, 2015

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Jun 16th, 2015
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Jun 16th, 2015
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