Answer
a) Vertex: $(-10000,5000)$
b) Wide.
c) Downward
d) $X_{min} = -15000, X_{max} = 0, Y_{min} = -1000, Y_{max} = 5000$
Work Step by Step
Given $$\begin{aligned}
f(x) &= -0.0005(x+10000)^2+5000.
\end{aligned}$$ a) The vertex of the parabola can be easily read from the above equation to be the point $(-10000,5000)$.
b) We see that the value of the multiplying constant is $a = 20$. Since the absolute value of $|a| = |-0.0005|= 0.0005< 1$, the parabola is wide compared to $f(x) = x^2$.
c) Since the constant $a$ is a negative number, the parabola will open downward.
d) Use your calculator to determine a suitable graphing window for the parabola. Here is a suggestion. $$\begin{aligned}
X_{min} &= -15000\\
X_{max}& = 0\\
Y_{min}& = -1000\\
Y_{max}& = 5000.
\end{aligned}$$
