Answer
a) Vertex: $(-30,-50)$
b) The shape of the parabola is unchanged.
c) Upward
d) $X_{min} = -60, X_{max} = 0, Y_{min} = -70, Y_{max} = 900$
Work Step by Step
Given $$\begin{aligned}
f(x) &= (x+30)^2-50.
\end{aligned}$$ a) The vertex of the parabola can be easily read from the above equation to be the point $(h,k)=(-30,-50)$.
b) We see that the value of the multiplying constant is $a = 1$. This means that the shape of the parabola remains unchanged.
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. $$\begin{aligned}
X_{min} &= -60\\
X_{max}& = 0\\
Y_{min}& = -70\\
Y_{max}& = 900.
\end{aligned}$$
