Theory question 101
FunctionsA function f is defined on the set R, of real numbers by f : x → px2 + qx + 2, where p and q are constants. If f(−2) = 0 and f(1) = 3, find f(−4)
Show the model answer
Model answer
f(−2) = 4p − 2q + 2 = 0, so 2p − q = −1
f(1) = p + q + 2 = 3, so p + q = 1
Adding: 3p = 0, so p = 0 and q = 1
f(x) = x + 2, so f(−4) = −2
Explanation
Form two equations from the given values, solve for p and q, then substitute x = −4.