Work Step by Step
We are given the function: $f(x)=-x^2-2x$ Rewrite the function building the square: $f(x)=-(x^2+2x+1)+1=-(x+1)^2+1$ We start by graphing the parent function $a(x)=x^2$. Then horizontally shift $a(x)$ one unit to the left to get $b(x)=(x+1)^2$. Then reflect $b(x)$ across the $x$-axis to get $c(x)=-(x+1)^2$. Finally, vertically shift $c(x)$ one unit upward to get $f(x)=-(x+1)^2+1$.