# Graphing function

• Oct 17th 2009, 09:40 AM
md56
Graphing function
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).
https://webwork.uncc.edu/webwork2_co...ob30image1.png

The answer I keep getting is -(x^2-4)+8, but that is incorrect. Please help me understand why.
• Oct 17th 2009, 09:53 AM
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
• Oct 17th 2009, 09:56 AM
ramiee2010
Quote:

Originally Posted by md56
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).
https://webwork.uncc.edu/webwork2_co...ob30image1.png

The answer I keep getting is -(x^2-4)+8, but that is incorrect. Please help me understand why.

$\displaystyle f(x)=x^2-4 \ is \ a\ parabola\$
http://www2.wolframalpha.com/Calcula...image/gif&s=14
$\displaystyle so\ on\ flip\ it\ vertically,\ and\ then\ move\ it\ up\ 8\ units\quad g(x)=-(x^2-4)+8$
• Oct 17th 2009, 10:01 AM
md56
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)