I am to take f(x)=x^2-4, flip it vertically, then move it up 8 units.
Here is the picture of the graph, I am supposed to match f(x) to g(x).
The answer I keep getting is -(x^2-4)+8, but that is incorrect. Please help me understand why.
Why is it incorrect?
If you meant "reflect it with respect to the x-axis" then
y = x^2 - 4 is translated to -y = x^2 - 4
so then you have y = -x^2 + 4
moving it up 8 units is a vertical translation of 8, so y = -x^2 + 12. (which is what you have but not simplified)
If it was meant to be read reflection about the y-axis, then x -> -x, so that y = x^2 - 4. add 8 makes it y = x^2 + 4
Oh I see my mistake. Though I do not entirely understand why it is a mistake. Why is the negative not distributed to the 4 if to flip a function vertically you must -f(x)