SOLUTION: Solve for A if f(x)=-Ax^2+Bx-8, f(-5)=-123 and g(x)=4x+B, g(2)=11

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Question 1095894: Solve for A if f(x)=-Ax^2+Bx-8, f(-5)=-123 and g(x)=4x+B, g(2)=11
Answer by MathTherapy(10801) About Me  (Show Source):
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Solve for A if f(x)=-Ax^2+Bx-8, f(-5)=-123 and g(x)=4x+B, g(2)=11
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Solve for A if system%28f%28x%29+=+-+Ax%5E2+%2B+Bx+-+8%2C+f%28-+5%29+=+-+123%29 and system%28g%28x%29+=+4x+%2B+B%2C+g%282%29+=+11%29

              f%28x%29+=+-+Ax%5E2+%2B+Bx++-++8
           f%28-+5%29+=+-+A%28-+5%29%5E2+%2B+B%28-+5%29++-++8
           f(- 5) = - 25A - 5B - 8
           - 123 = - 25A - 5B - 8
    25A + 5B = 115 ------ eq (i)

            g(x) = 4x + B
            g(2) = 4(2) + B
               11 = 8 + B
                 3 = B

   25A + 5B = 115 ---- eq (i)
25A + 5(3) = 115 ---- Substituting 3 for B in eq (i)
   25A + 15 = 115
            25A = 100
             highlight%28highlight_green%28highlight%28A+=+100%2F25+=+4%29%29%29

        (A, B) = (4, 3)