Use a graphing calculator to plot the data and find the quadratic function of best fit.
-The number of housing starts in one beachside community remained fairly level until 1992 and then began to increase. The following data shows the number of housing starts since 1992 (x = 1). Use a graphing calculator to
Plot a scatter diagram. What is the quadratic function of best fit? $\begin{array}{l|l}
\text { Year, x } & \text { Housing Starts, H } \
\hline 1 & 200 \
2 & 210 \
3 & 230 \
4 & 240 \
5 & 250 \
6 & 230 \
7 & 215 \
8 & 208
\end{array}$
A) $\mathrm { H } ( \mathrm { x } ) = - 3.268 \mathrm { x } ^ { 2 } - 30.494 \mathrm { x } + 168.982$
B) $\mathrm { H } ( \mathrm { x } ) = - 3.268 \mathrm { x } ^ { 2 } + 30.494 \mathrm { x } - 168.982$
C) $\mathrm { H } ( \mathrm { x } ) = 3.268 \mathrm { x } ^ { 2 } + 30.494 \mathrm { x } + 168.982$
D) $\mathrm { H } ( \mathrm { x } ) = - 3.268 \mathrm { x } ^ { 2 } + 30.494 \mathrm { x } + 168.982$

Question

Quizplus · Accepted Answer

Given the nature of the data, which initially increases and then decreases, a quadratic function of best fit would likely have a negative coefficient for the $x^2$ term, indicating a parabola that opens downwards. Among the options, only choices with a negative coefficient for $x^2$ term are plausible. The correct quadratic function must accurately model the trend of the data, which increases to a peak and then decreases. Option D is the correct choice because it has the negative coefficient for the $x^2$ term, indicating the parabola opens downwards, and the positive linear coefficient and constant term align with the general increase before the peak and subsequent decrease in housing starts.

Use a Graphing Calculator to Plot the Data and Find