Answer
See image
Work Step by Step
Write $f$ in the form $f(x)=a(x-h)^{2}+k$:
$\begin{aligned}f(x)&=-x^{2}-2x\\&=-\left(x^{2}+2x\right)\\&=-\left(x^{2}+2x+1\right)+1\\&=-(x+1)^{2}+1\end{aligned}$
Let $f_{1}(x)=x^{2}$.
Then, $f(x)=-f_{1}(x+1)+1$.
The graph is obtained from $f_{1}(x)$ by
- reflecting about the x-axis $(x,y)\rightarrow(x,-y),$
- shifting to the left by 1 unit,
- and then up by 1 unit
Point by point,
$\left[\begin{array}{lllll}
(x,y) & \rightarrow & (x,-y) & \rightarrow & (x-1,-y+1)\\
& & & & \\
(0,0) & \rightarrow & (0,0) & \rightarrow & (-1,1)\\
(-1,1) & \rightarrow & (-1,-1) & \rightarrow & (-2,0)\\
(1,1) & \rightarrow & (1,-1) & \rightarrow & (0,0)\\
(-2,4) & \rightarrow & (-2,-4) & \rightarrow & (-3,-3)\\
(2,4) & \rightarrow & (2,-4) & \rightarrow & (1,-3)
\end{array}\right]$
