+921 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).
+130477 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
