9 A random number, x, is generated, where x is any real number. (a) Manuel adds 2 to x. He subtracts x from 10. Manuel then multiplies these two results to give his number, y. Show that y = 20 + 8x - x^2 . (b) On the grid opposite, draw the graph of y = 20 + 8x - x^2 for 0 =< x =< 10 . Four points have been plotted for you. (c) On the same grid, draw a suitable line to find the value of Manuel’s number, y, when it is the same as the random number, x. (d) Jolene multiplies the random number, x, by 5 and then adds 2 to give her number, z. Calculate the possible values of x when Manuel’s number, y, and Jolene’s number, z, are the same.