Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 104: 67

$f(x)=(x+1)^2-1$ See graph

We are given the function: $f(x)=x^2+2x$ Complete the square: $f(x)=x^2+2x+1-1=(x+1)^2-1$ We start graphing with the basic function $a(x)=x^2$. We horizontally shift $a(x)$ by one unit to the left to get $b(x)=(x+1)^2$. Then we vertically shift $b(x)$ one unit downward to get $f(x)=(x+1)^2-1$. We use 3 points: $(-1,-1),(0,0),(1,3)$