What happens on the graph when a polynomial function has a factor that occurs more than once?
If there is a factor that occurs more than once, then at that root (x-intercept), the graph locally resembles the parent graph that corresponds to the power of the factor. For example, if there is a double root, at that intercept, the graph would look quadratic (it would curve down to touch the x-axis, then turn and curve back, looking like a parabola in that area) If there is a triple root, the graph would look like a cubic (it makes a kind of “squiggle” when it gets close to the intercept, but instead of turning around, like on a double root, it goes through the x-axis) Higher powers, if they are even, look similar to the double root, just flatter close to the x-axis. If the powers are odd, they look like the triple root, just flatter by the axis.
