How does a quartic function with 4, equal real roots look like?

Question

hartnn · Answer

since they are equal roots, let them all be a.  where a is real.
now there are 4 roots,
so (x-a)^4=0
it will look like this.

anonymous · Answer

Alright, how does the graph look like now?

anonymous · Answer

No longer a quadratic, but:

$$f(x) = (x+1)^4$$
Is one example.

The general form is 
$$f(x) = (x+a)^4$$
where "a" is any constant, and the solution will be -a.

anonymous · Answer

The graph will look like this: http://www.wolframalpha.com/input/?i=%28x%2B1%29%5E4 (For my example of $$f(x) = (x+1)^4$$) Note that for any function with multiple equivilant roots, the graph will "touch" the y-axis without crossing it.

hartnn · Answer

the graph of f(x)=(x-a)^4 will have one x-intercept of (a,0).

anonymous · Answer

* The graph will touch without crossing the x-axis for any even number of equivilant roots. Sorry for the confusion.

anonymous · Answer

Does the graph get wider as the exponent n  increases for a function with n roots?

anonymous · Answer

Yes.

anonymous · Answer

Thanks

anonymous · Answer

Ugh if i can only give medals to both of you instead of just one