Stuck on how to start this transformed function problem

[peppercorn]

The question I'm trying to answer uses the info from this graph. I converted f(x)=4x^2+8x-5 to f(x)=4((x+1)^2)-9.


I first tried to change y=-3f(2x)+4 to general form but I'm confused because I don't see how the background info has anything to do with this question.


What first steps should I follow?

 

[Dr.Peterson]

I think you may be misreading the problem.

They have told you that f(x) = 4x^2+8x-5. Now they are asking you for the equation of a new function we could call g(x) = -3f(2x) + 4.

So first find f(2x) by simply replacing x in the given function with (2x), and simplify that. Then put that in place of f(2x) in the equation of f(x), and simplify.

 

[peppercorn]

I think you may be misreading the problem.

They have told you that f(x) = 4x^2+8x-5. Now they are asking you for the equation of a new function we could call g(x) = -3f(2x) + 4.

So first find f(2x) by simply replacing x in the given function with (2x), and simplify that. Then put that in place of f(2x) in the equation of f(x), and simplify.

So I replace x with 2x in g(x) = -3f(2x)+4 and simplify, and then use what I get from that to do the same thing in f(x) = 4x^2+8x-5 ?

 

[Dr.Peterson]

No, that doesn't sound like what I said. Just replace x with 2x in f(x) = 4x^2+8x-5, making f(2x) = ... . Then put that into g(x) = -3f(2x)+4 .

To make clear whether you are thinking the right thing, please actually do it and show what you get, rather than just describing it.

 

[peppercorn]

Ok thank you. I've figured it out now and where I went off track.