The table gives the average price (in dollars) for a gallon of regular unleaded gasoline as measured in September of the years 2003 to 2009. (Source: The Bureau of Labor Statistics, 2009)

(a) Plot the data letting $x=3$ represent 2003, $x=4$ represent 2004, and so on.
(b) Find a function of the form $f(x)=a(x-h)^{2}+k$ that models this data. Let $(8,3.70)$ represent the vertex, and use $(3,1.73)$ to determine the value of $a$.
(c) Use the statistical capability of a graphing calculator to find the best-fitting quadratic function, $g$, for this data. Graph both functions $g$ and $f$ from part (b) in the same window as the data points. Which function is the better fit?

Question

The table gives the average price (in dollars) for a gallon of regular unleaded gasoline as measured in September of the years 2003 to 2009. (Source: The Bureau of Labor Statistics, 2009)
  
(a) Plot the data letting $x=3$ represent 2003, $x=4$ represent 2004, and so on.
(b) Find a function of the form $f(x)=a(x-h)^{2}+k$ that models this data. Let $(8,3.70)$ represent the vertex, and use $(3,1.73)$ to determine the value of $a$.
(c) Use the statistical capability of a graphing calculator to find the best-fitting quadratic function, $g$, for this data. Graph both functions $g$ and $f$ from part (b) in the same window as the data points. Which function is the better fit?

Quizplus · Accepted Answer

The Answer of The table gives the average price (in dollars) for a gallon of regular unleaded gasoline as measured in September of the years 2003 to 2009. (Source: The Bureau of Labor Statistics, 2009)
  
(a) Plot the data letting $x=3$ represent 2003, $x=4$ represent 2004, and so on.
(b) Find a function of the form $f(x)=a(x-h)^{2}+k$ that models this data. Let $(8,3.70)$ represent the vertex, and use $(3,1.73)$ to determine the value of $a$.
(c) Use the statistical capability of a graphing calculator to find the best-fitting quadratic function, $g$, for this data. Graph both functions $g$ and $f$ from part (b) in the same window as the data points. Which function is the better fit?

The Table Gives the Average Price (In Dollars) for a Gallon