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Suppose f(x) is a quadratic function such that f(1) = -24, f(4) = 10, and f(3) = 60.

 

Determine the value of f(-1).

 Feb 19, 2025
 #1
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a(1)^2 + b(1) + c =  -24

a(4)^2 + b(4) + c = 10

a(3)^2 + b(3) + c = 60         simplify these

 

a +  b +  c =  -24           (1)

16a + 4b + c = 10          (2)

9a + 3b + c = 60            (3)

 

Subtract (2) - (1)  and (3) -(1)

 

15a + 3b  = 34     (4)

8a + 2b  =  84  →  4a + b  = 42  →  b = 42 - 4a       (5)

 

Sub (5)  into (4)

15a + 3(42 - 4a)  =  34

15a + 126 -12a = 34

3a  = -92

a = -92/3

 

b = 42 - 4(-92/3)  = 494/3

 

a + b + c =  -24

-92/3 + 494/3 + c = -24

c = -24 + 92/3  - 494/3   = -158

 

f(-1)  = (-92/3)(-1)^2  + (494/3)(-1)  - 158  =   -1060 / 3 

 

 

cool cool cool

 Feb 19, 2025

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