The height, y m, of a rider above the ground in a section of roller coaster ride is given by y = 1/3*x^2 - 2x + 8, where x m is the rider's horizontal disantce form the start of the ride.
i) y = 1/3 x^2 -2x + 8
= 1/3 (x^2 - 6x) + 8
=1/3 ( x - 3)2 + 8 - 3
= 1/3 (x-3)2 + 5
ii) Min will occur at vertex 3,5 5 m
iii) put in 8 for 'y' and calculate 'x' into the equation in i) or the origianl equation given in the Q