So first question, when I am evaluating f(x+1) and I end up with -x^2+4x+3 how can I get rid of that negative? can I put a positive in front and switch 4 and 3 to negative? I know thats a pretty basic question but I can't figure it out.
Why does it need to be negative? If you need to, you can factor out a -1, so -1(x^2-4x-3)
Second question, the problem is: Sketch the graph of f(x) x^4-5x^2+4 by factoring the function first. Label all intercepts. Obviously you guys can;t show me how to graph because they are pretty complex but for the factoring I need help. I got that a factor of it is 1.
(x^2-4)^2+(x^2-1)^2. So your intercepts are +-2 and +-1.
after synthetic division or substitution (don't know which one it is haha) the quotient on the bottom is 1 1 -4. Which turns into x^2+x-4, but where do I go from there? Is 1 a triple root. No other factors worked. Not either positive or negative 4 or 2. So i'm pretty confused here.
What is the question here?
Third question, when sketching y=x^3-4x. I did....
take out an x: x(x^2-4)
so some intercepts are o,2, and -2. And I know the height is 4 but is it negative or positive. I can't tell if it switches like when they are in the parenthesis.
The height? I'm not sure what you are asking. The critical points are +-(4/3)^(1/2), and f(x) is positive at the negative one and negative at the positive one.