A function F is defined on the set R, of real numbers by (f : x to px^{2} + qx + 2), where p and q are constants. If (f(-2) = 0) and (f(1) = 3), find (f(-4)).
Explanation
(f(x) = px^{2} + qx + 2)
(f(-2) = p(-2)^{2} + q(-2) + 2 = 0)
(4p – 2q + 2 = 0)
(implies 4p – 2q = -2 … (1))
(f(1) = p(1)^{2} + q(1) + 2 = 3)
(p + q + 2 = 3)
(implies p + q = 1 … (2))
From (2), (q = 1 – p). Substitute for q in (1).
(4p – 2(1 – p) = -2 implies 4p – 2 + 2p = -2)
(6p = 0 implies p = 0)
(q = 1 – p = 1 – 0 = 1)
(therefore f(x) = x + 2)
(f(-4) = -4 + 2 = -2)