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? $\begin{array}{l|l}
\text { Year, x } & \text { Housing Starts, H } \
\hline 1 & 200 \
2 & 205 \
3 & 210 \
4 & 240 \
5 & 245 \
6 & 230 \
7 & 220 \
8 & 210
\end{array}$
A) $H ( x ) = - 2.679 x ^ { 2 } + 26.607 x + 168.571$
B) $H ( x ) = - 2.679 x ^ { 2 } + 26.607 x - 168.571$
C) $\mathrm { H } ( \mathrm { x } ) = 2.679 \mathrm { x } ^ { 2 } + 26.607 \mathrm { x } + 168.571$
D) $\mathrm { H } ( \mathrm { x } ) = - 2.679 \mathrm { x } ^ { 2 } - 26.607 \mathrm { x } + 168.571$

Question

Quizplus · Accepted Answer

The quadratic function of best fit for the given data, when plotted on a graphing calculator, typically has a negative coefficient for the $x^2$ term if the data shows an initial increase followed by a decrease, as indicated by the housing starts peaking and then declining. The positive linear coefficient suggests an initial increase, and the positive constant term fits the starting value. Option A has these characteristics, making it the most plausible quadratic function of best fit.

Use a Graphing Calculator to Plot the Data and Find