Answer
a) Vertex: $(0,200)$
b) Wide
c) Downward
d) $X_{min} = -200, X_{max} = 200, Y_{min} = 0, Y_{max} = 200$
Work Step by Step
Rewrite the given equation of the parabola so that it looks exactly like the general standard vertex form, $ f(x) = a(x-h)^2+k$.
$$\begin{aligned}
f(x) &= -0.01x^2+200\\
& = -0.01(x-0)^2+200.
\end{aligned}$$ a) The vertex of the parabola can be easily read from the above equation to be the point $(h,k)=(0,200)$.
b) We see that the value of the multiplying constant is, $a = -0.01$. Since the absolute value of, $|a| = |-0.01|=0.01 < 1$, the parabola is wider 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.
$$\begin{aligned}
X_{min} &= -200\\
X_{max}& = 200\\
Y_{min}& = 0\\
Y_{max}& = 200.
\end{aligned}$$
