Question

Answer the following:

If f(x) = ax² + bx + 2 and f(1) = 3, f(4) = 42, find a and b

Answer 1

f(x) = ax² + bx + 2

f(1) = 3

∴ a(1)² + b(1) + 2 = 3

∴ a + b = 1    ...(i)

f(4) = 42

∴ a(4)² + b(4) + 2 = 42

∴ 16a + 4b = 40

Dividing by 4, we get

4a + b = 10   ...(ii)

Solving (i) and (ii), we get

a = 3, b = –2