Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 104: 70

$f(x)=(x+2)^2-2$ See graph

We are given the function: $f(x)=x^2+4x+2$ Complete the square: $f(x)=x^2+4x+4-4+2=(x+2)^2-2$ We start graphing with the basic function $a(x)=x^2$. We horizontally shift $a(x)$ by 2 units to the left to get $b(x)=(x+2)^2$. Then we vertically shift $b(x)$ 2 units downwards to get $f(x)=(x+2)^2-2$. We use 3 points: $(0,2),(-2,-2),(-4,2)$.