Question

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`?

Answer 1

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.

Explanation:

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

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: