algebra

Have a few questions can someone please help me figure them out?

1) You research the cost of a gallon of gasoline over several years to look for a trend. The table shows your data. What is a line of best fit for the data? Based upon these prices, how much would you expect tp pay in 2026?

Year
1980 1984 1988 1992 1996 2000 2004 2008 2012
Price per Gallon
1.25 1.27 1.05 1.28 1.43 1.68 2.11 3.72 3.99

possible answers
y=0.347x+0.856;9.88
y=.087x-171.26;5.01
y=0.134x+1.25;7.41
y=0.087x+0.587;4.59

2) ompare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformations of the parent function?
y=[8x-2]-7

possible answers;
(-1/4,-7)
x=-1/4
translated to the right 1/4 units and up 7 units

(1/4,7)
x-1/4
translated to the right 1/4 units and up 7 units

(-1/4,7)
x=-1/4
translated to left 1/4 units and up 7 units

(1/4,-7)
x=1/4
translated to the right 1/4 units and down 7 units

3) You live near a bridge that goes over a river. The underside of the bridge is an arch that can be molded with function y=-0.000471x^2+.837x where x and y are measured in feet. How high above the river is the bridge(the top of the arch)? How long is the section of the bridge above the arch?

possible answers;

the bridge is about 1,777.07 above and the length is about 888.54 ft

the bridge is about 371.85 ft above and the length is about 1,777.07 ft

the bridge is about 371.85 ft above and the length is about 888.54 ft

the bridge is about 1,777.07 ft above and the length is about 371.85 ft

I hope someone can help me figure these problems out I missed them on quiz and trying to figure them out.

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  1. 1)
    without actually doing a regression, I'd pick the 2nd choice. The rise averages only $.065/yr, so I'd not expect it to more than double in the next 10 years.

    2)
    there's a typo, since no parabola is given, but the 8x-2 indicates a shift of 1/4 to the right, and then down 7.
    (d)

    3)
    y = x(.837-.000471x)
    so the roots are at x=0 and x=1777.07, so that's the length. (b)
    No other choice fits, but as a check, y(888.53) = 371.85

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  2. Thanks Steve for the help

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