SOLUTION: the table shows the average fuel consumption ( in gallons) of a passenger car between 1970 and 1996 ------------------------------------------------- year,t(x)**0**5**10*

Question 120911: the table shows the average fuel consumption ( in gallons) of a passenger car between 1970 and 1996

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year,t(x)**0**5**10**15**20**25**26
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average fuel
consumption, **760**695**576**559**520**530**531
F(y)
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sorry for the above it is meaning to be a table telling the X and Y points and the stars are seperating the numbers
so the question is
1) Write quadratic model for the average fuel consumption F, as a function of time T, where T is the number of years since 1970.
i greatly appreciate the help
Answer by scott8148(5891) (Show Source):
You can put this solution on YOUR website!
the equation is of the form ax^2+bx+c

F=aT^2+bT+c __ when T is zero, F=760; so c=760

F=aT^2+bT+760 __ use two other points to generate two equations for a and b

695=25a+5b+760 __ multiplying by 2 gives 1390=50a+10b+1520 __ -130=50a+10b

576=100a+10b+760 __ -184=100a+10b

subtracting the equations will eliminate the b
__ once you have a, then substitute to find b