Flip, Then Shift

Flips and shifts combine, and the rule tells you the order. In y = -f(x) + 5 with f(x) = x^2, you work out f(x), make it negative, then add 5. So the graph flips first and then moves up 5.

Follow the vertex: (0, 0) flips to (0, 0), then rises to (0, 5). One step right, f gives 1, the flip gives -1, and adding 5 gives 4: the point (1, 4). The curve opens down from its top point at (0, 5).

Compare y = -(f(x) + 5). Here the brackets add 5 first and the minus flips the result, so the top point lands at (0, -5). Read the rule the way you would work out a number, and the order of the moves comes with it.