Question

Optimisation problem:

What is the minimum vertical distance between the parabolas y = x 2 + 1 and y = x - x^2 ?

Answer 1

Minimum Distance would be a challenging problem. Minimum Vertical Distance is just subtraction. x^2 + 1 > x - x^2 for every value of x, thus, we must minimize (x^2 + 1) - (x - x^2) = 2x^2 - x + 1. Given the new parabola, y = 2x^2 - x + 1, can you find the vertex?