Answer
Model: $ f(x) = -0.4(x+5)^2$
Domain: All real numbers
Range: $(-\infty,0 ]$
Work Step by Step
Step 1: Make a scatter plot of the data and choose a vertex point that may either be the lowest or highest point. The vertex of the data point can be seen to be at $(h,k)=(-5,0)$.
Step 2: Set these into the standard vertex form of a parabola. This gives: $$\begin{aligned}
f(x) &= a(x+5)^2.
\end{aligned}$$ Step 3:
Choose any point from the scatter plot to find the value of the constant $a$. Let's take the point $(x,y)=(0,-10)$ and insert this into the above equation to find $a$. $$\begin{aligned}
-10 &= a(0+5)^2\\
-10& = 25a\\
a& = -0.4
\end{aligned}$$ Hence, the parabola that best fit the data is $$f(x) = -0.4(x+5)^2.$$ The domain and range of this function are:
Domain: All real numbers,
Range: $(-\infty,0 ]$.
Plot the function and see if it fits the data.
