A process used to make a quadratic expression into a perfect square trinomial is called

It is completing the square. Very useful since it finds the min or max.

y = x^2 + 8x + 17

y = (x^2 + 8x + ...) + 17

y = x^2 + 8x + (8/2) ^2 + 17 - 4^2

y = (x^2 + 8x + 4^2) + 17 - 16

y = (x^2 + 8x + 16) + 1

y = (x + 4) ^2 + 1

This means that the graph has a minimum at (-4, 1) Check it out on the graph I've given you.