Chapter 0 - Before Calculus - 0.2 New Functions From Old - Exercises Set 0.2 - Page 25: 20

Check attached graph.

To undertand the graph of $\sqrt(x^{2} - 4x + 4)$, we divide it into three parts. Part 1: $x^{2}$: this is relatively simple to understand. It is an upward-facing parabola with the bottom of the curve at (0,0). Part 2: $x^{2} - 4x$: this shifts the bottom-most part of the curve (also called the minima) to (2, -4). Part 3: $x^{2} - 4x + 4$: adding the constant $4$ shifts the curve up by four units, that is, the y coordinate goes from -4 to 0. Thus, the minima of the curve now becomes (2, 0). Part 4: $\sqrt(x^{2} - 4x + 4)$: Taking the square root of this does not change the coordinates of the bottom-most part - minima. But, it changes the shape of the curve. It now looks like a |x| curve with some slight changes.