From your part one expression which is -2 (x - 1)^2 + 8,

Greatest value of this expression is -2 (0) + 8 = 8.

This is because the minimum output value of a squared expression (x - 1)^2 is 0 (when x = 1) and thus multiplying this by a negative number makes the minimum become a maximum.

So, the greatest value of 3^that expression is 3^8 = 6561.

For the third part, I see -2 (x + 1) (x - 3) and -2 (x - 1)^2 + 8.

We use both forms to our advantage.

From the original form, we can deduce that the graph is a sad face, since the coefficient is -2 and the x-intercepts are at (-1, 0) and (3, 0).

From the second form, we see that (1, 8) is our maximum turning point and (0, 6) is our y-intercept.

We plot these four points on the graph and connect them with a sad face graph which turns at (1, 8).

Thank you. Clearly understood. But partiii

I plot when I have paper later and no one else has done them (I can’t sketch them in this text).

I am out without writing stuff at the moment.

You can use Desmos graphing software online to help you sketch the graph if you are in urgent need of drawing the graph.