Quick Graphing Question???

[Chucknoddis]

Hello, I have a quick question with my math problem and was hoping someone here might have the solution. I currently have the graph of x^3-12x^2 and need to find a formula for its flipped transition. I have included the graph below that requires a formula. If anyone could help me out with this I would be very thankful.

 

[stapel]

I have included the graph below....

....freemathhelp.com/forum/webkit-fake-url://6F537AFA-6B95-4DAE-9964-67A545839D03/jlpeeple-4939-setSection_1-Q-2prob2image2.png

Your copy-n-paste from your local environment is not porting over properly. Please post your image elsewhere and provide a link here to the location. Thank you.

 

[HallsofIvy]

I don't know what you mean by "flipped transition". "Flipped" around what line? And I suspect that "transition" is not the right word. If you mean "flipped around the x-axis" (I would say reflected in the x-axis) then multiply the function by -1: \(\displaystyle -x^3+ 12x^2\).

 

[Chucknoddis]

Sorry, you are probably correct about the wording, however I am confused on the exact equation for that graph. Multiplying the equation by (-1) does not give me the correct equation, as when plugged in, it does not match up with the graph I have posted. Is there a way to identify the equation by just looking at the graph?

 

[DrPhil]

Sorry, you are probably correct about the wording, however I am confused on the exact equation for that graph. Multiplying the equation by (-1) does not give me the correct equation, as when plugged in, it does not match up with the graph I have posted. Is there a way to identify the equation by just looking at the graph?

The plot you made is related to (but not equal to) the formula \(\displaystyle f(x) = x^3 - 12x^2\). The first thing I notice is that the curve doesn't pass through the origin, but is shifted downward by 64 units.

The next thing I see is that the behavior at large x, + or -, is in the negative direction. That requires the function to be flipped around one axis or the other. Changing the sign of \(\displaystyle f(x)\) and shifting \(\displaystyle -64\) gives

\(\displaystyle g(x) = -x^3 + 12 x^2 - 64\)

Check all the given points to see if that is the answer. You also have to make sure the zeros of the derivative are at the right places.