Aprocess 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.