Answer
a) Vertex: $(55.8,-29.7)$
b) No change in the shape of the parabola
c) Upward
d) $X_{min} = 40, X_{max} = 75, Y_{min} = -35, Y_{max} = 180$
Work Step by Step
Given $$\begin{aligned}
f(x) &= (x-55.8)^2-29.7.
\end{aligned}$$ a) The vertex of the parabola can be easily read from the above equation to be the point $(55.8,-29.7)$.
b) We see that the value of the multiplying constant is $a = 1$.This means that the parabola is neither wide nor 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. $$\begin{aligned}
X_{min} &= 40\\
X_{max}& = 75\\
Y_{min}& = -35\\
Y_{max}& = 180.
\end{aligned}$$
