Quadratic Functions

Question

Determine two consecutive odd integers such that the sum of their squares is a minimum.

Answer 1

Let is first, then (x + 2) is second.

F(x ) = x² + (x + 2)² = 2x² + 4x + 4. This is quadratic function. It has minimum at vertex of parabola, so x =

- b/(2a) = -4/4 = - 1. So first number x = - 1, x + 2 = - 1 + 2 = 1

Answer: -1, 1