A quadratic function f(x) attains a maximum of 3 at x = 1

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value f(x) at x = 10?

  1. -180
  2. -159
  3. -110
  4. -119

Answer

Let a quadratic function f(x) = ax2 + bx + c

At x = 1, f(1) = a + b + c = 3 (Maximum value of function)

At x = 0, f(0) = c = 1

a + b = 2 or b = 2 - a

The maximum of the function f(x) is attained at

x = - b/2a = 1 = (a - 2)/2a

a = -2 and b = 4

Therefore f(x) = -2x2 + 4x + 1

f(10) = -159

The correct option is B.