Answer
a) Vertex: $(-25000,-10000)$
b) Narrow
c) Downward
d) $X_{min} = -25,500, X_{max} = -24,500, Y_{min} = -100,000, Y_{max} = 0$
Work Step by Step
Given $$\begin{aligned}
f(x) &= -10(x+25000)^2-10000.
\end{aligned}$$ a) The vertex of the parabola can be easily read from the above equation to be the point $(-25000,-10000)$.
b) We see that the value of the multiplying constant is $a = -10$. Since the absolute value of $|a| = |-10|= 10> 1$, the parabola is narrow 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. $$\begin{aligned}
X_{min} &= -25500\\
X_{max}& = -24,500\\
Y_{min}& = -100,000\\
Y_{max}& = 0.
\end{aligned}$$
