Question

Determine a quadratic function (f) is defined by f (x) = ax² + b + c. If f (0) = 6, f(2) = 1, f(– 3) = 6

Answer 1

Given, f (x) = ax² + bx + c. 

At x = 0, f(0) = 6 (given) 

∴ a × 0 + b × 0 + c = 6 

∴ c = 6    (i) 

At x = 2, f(2) = 1 (given) 

∴ a(2)² + b(2) + c = 1 

⇒ 4a + 2b + 6 = 1 (using (i)) 

⇒ 4a + 2b = – 5 (ii) 

At x = – 3, f(–3) = 6 

∴ a(– 3)² + b(– 3) + c = 6 

⇒ 9a – 3b + 6 = 6 (using (i)) 

⇒ 9a – 3b = 0 (iii) 

On solving eqs. (ii) And (iii), we get

a = \(-\frac{1}{2}\) and a = \(-\frac{3}{2}\) ∴ Required quadratic function (f) = \(\frac{-1}{2}\) x² + \(\frac{-3}{2}\)x + 6