Answer
a) Vertex: $(0,100)$
b) Narrow
c) Upward
d) $X_{min} = -10, X_{max} = 10, Y_{min} = 0, Y_{max}= 600$
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$.
$$\begin{aligned}
f(x) &= 5x^2+100\\
& = 5(x-0)^2+100.
\end{aligned}$$ a) The vertex of the parabola can be easily read from the above equation to be the point, $(h,k)=(0,100)$.
b) We see that the value of the multiplying constant is $a = 5$. Since the absolute value of $|a| = |5| > 1$, the parabola is narrow compared to $f(x) = x^2$.
c) Since the constant $a$ is a positive number, the parabola will open upward.
d) Use your calculator to determine a suitable graphing window for the parabola. Here is a suggestion. $$\begin{aligned}
X_{min} &= -10\\
X_{max}& = 10\\
Y_{min}& = 0\\
Y_{max}& = 600.
\end{aligned}$$
