How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given #y=x(x+1)^2(x+4)^2#?

1 Answer
Dec 8, 2016

End behavior will follow the "parent graph" y = #x^5# since all of the factors multiplied out would have that degree. That means falling to the left and rising to the right.


If you wish to write the end behavior in formal notation, it would look like: my image

The x-intercepts would be 0, -1, and -4 by the Zero Product Property.

The graph would cross at 0, and be tangent (or touch and turn around) at -1 and -4 since the factors appear an even number of times.

The y-intercept is found by evaluating at x = 0: y = #0(1)(16)=0#
(The origin is both the x- and y-intercepts)

Here is the graph: my image