Explain how you can determine if a linear factor of a function is squared or cubed by examining the graph of the function.

Halp I don't know :|

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  1. If a linear factor is a single root, the graph crosses the x-axis there, at some sloping direction.

    If it is a double root (or some higher even order), the graph just touches the x-axis

    If it is a triple root (or higher odd order), it crosses the x-axis, but is also tangent to it.

    Think of familiar graphs you know. A parabola with two roots crosses the x-axis, but if it has a double root, it just touches it.

    y=x^3 cross the axis, but makes a little jog there so the slope is horizontal as it crosses.

    y=x^4 looks like a squarer parabola, again just touching the x-axis.

    Think of a double root. It's just the limit of what happens when there are two roots which get closer and closer together. Instead of crossing the axis and back, the graph just touches it before reversing direction.

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