Answer
(a) $y = -275.43x^2 + 19749x - 273552$
(b) See graph.
(c) $33.85lb/in^2$
Work Step by Step
(a) Find the quadratic polynomial that best fits the data.
$y = -275.43x^2 + 19749x - 273552$
(b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data.
See graph.
(c) Use your result from part (b) to estimate the pressure that gives the longest tire life.
With the graph, we can find the maximum of tire life happens when $x=33.85lb/in^2$
