Use a graphing calculator to plot the data and find the quadratic function of best fit.
-An engineer collects data showing the speed s of a given car model and its average miles per gallon M. Use a graphing calculator to plot the scatter diagram. What is the quadratic function of best fit? $\begin{array}{l|c}
\text { Speed, s } & \text { mph, M } \
\hline 20 & 18 \
30 & 20 \
40 & 23 \
50 & 25 \
60 & 28 \
70 & 24 \
80 & 22
\end{array}$
A) $\mathrm { M } ( \mathrm { s } ) = 0.063 \mathrm { x } ^ { 2 } + 0.720 \mathrm { x } + 5.142$
B) $\mathrm { M } ( \mathrm { s } ) = - 6.309 \mathrm { x } ^ { 2 } + 0.720 \mathrm { x } + 5.142$
C) $M ( s ) = - 0.0063 x ^ { 2 } + 0.720 x + 5.142$
D) $M ( s ) = - 0.631 x ^ { 2 } + 0.720 x + 5.142$

Question

Quizplus · Accepted Answer

Given the data, a quadratic function of best fit is typically found using a graphing calculator's regression feature. The correct function, $M(s) = -0.0063s^2 + 0.720s + 5.142$, accurately reflects a quadratic relationship where the coefficient of $s^2$ is negative, indicating a parabolic shape that opens downwards, which is consistent with the general trend of increasing miles per gallon up to a certain speed before it starts to decrease, as seen in the provided data.

Use a Graphing Calculator to Plot the Data and Find