A random number, x, is generated, where x is any real number.

1. (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 − x² .[2]
2. (b)On the grid opposite, draw the graph of y = 20+ 8x-x² for 0≤x≤ 10. Four points have been plotted for you.[4]
3. (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.[2]
4. (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.[4]

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