Car tires need to be inflated properly. Overinflation or underinflation can cause premature treadwear. The data below show tire life for different inflation values for a certain type of tire. Pressure Tire Life (Ib/in²) (mi) 26 50,000 28 66,000 31 78,000 35 81,000 38 75,000 42 70,000 45 60,000 (a) Find the quadratic polynomial that best fits the data. (Let y be the tire life in miles and x the pressure in Ib/in². Round all numerical values to three decimal places.) (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. y (mi) y (mi) 80 000 60 000 80 000 60 000 40 000 40 000 20 000 20 000 49/in 50 20 49b/ in 10 20 30 10 30 - 20 000| O-20000| y (mi) y (mi) 80 000 80000 60 00 60 000 40 000 40 000 20 000 20000 20 49b/in 20 49b/ in50 10 30 10 30 – 20 000| - 20000| (c) Use your result from part (b) to estimate the pressure that gives the longest tire life. (Round your answer to two decimal places.) Ib/in?

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