Question

Minimze the product of a positive rational number and a negative rational number, given that the positive number is exactly 8 greater than the negative number. what is the final product?

Answer 1

If we let x represent the negative rational number, then the product is
x(x+8)
This describes an upward-opening parabola whose vertex is (-4, -16).

The numbers are -4 and +4, and the final product is -16.