Answer
See image:
Work Step by Step
$ \begin{array}{llll}
\text{Function:} & f(x)=-x^{2}-40x+500 & & \\
\text{coefficients} & a =-1, b=-40, c=500 & & \\
\text{coefficient a} & \text{negative, opens down} & \\ & \\
\text{Vertex} & x_{V}=-b/(2a) & y_{V}=f(-b/(2a) & \\
& x_{V}=-20 & y_{V}=900 & \\
& \bf V(-20,900) & & \\\\
\text{Line of symmetry} & x=-20 & & \\
\text{y intercept} & c=500, & \bf(0,500) & \\
\text{point symmetric to } & & & \\
\text{the y-intercept} & x=2x_{V}=-40 & \bf(-40,500)\\ & \\
\text{Zeros:} & -x^{2}-40x+500=0 & & \\
& -(x^{2}+40x-500)=0 & [50\times(-10)=500] & \\
& -(x+50)(x-10)=0 & [50+(-10)=40] & \\
& x=-50, x=10 & & \\
& \bf(-50,0), (10,0) & &
\end{array}$
Using the above information, plot the points and join with a smooth curve (parabola).