(a)[2]
Manuel increases $x$ by $2$. He then subtracts $x$ from $10$. Manuel then multiplies these two results to produce his number, $y$. Show that $y=20+8x-x^2$.
(b)[4]
On the grid opposite, plot the graph of $y=20+8x-x^2$ for $0\le x\le10$. Four points are already marked for you.
(c)[2]
On the same grid, draw a suitable line to determine the value of Manuel’s number, $y$, when it is equal to the random number, $x$.
(d)[4]
Jolene multiplies the random number, $x$, by $5$ and then adds $2$ to produce her number, $z$. Calculate the possible values of $x$ when Manuel’s number, $y$, and Jolene’s number, $z$, are equal.