Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding - Page 258: 70

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

Completing the square: $f(x)=x^2+4x+2$ $f(x)=x^2+4x+(\frac{4}{2})^2-(\frac{4}{2})^2+2$ $f(x)=x^2+4x+2^2-2^2+2$ $f(x)=(x+2)^2-4+2$ $f(x)=(x+2)^2-2$ Graphing the function: 1st step (black graph): The parent function: $y=x^2$ 2nd step (green graph): Shift down by 2 units. $y=x^2-2$ Final step (blue graph): Shift left by 2 units. $y=(x+2)^2-2$