Give an example of a quadratic equation with a double root, and state the
relationship between the double root and the graph of the related function.
The two roots are equal. The factors will be (x − a)(x − a), so that the two roots are a, a.
For example, this quadratic
x² − 12x + 36
can be factored as
(x − 6)(x − 6).
If x = 6, then each factor will be 0, and therefore the quadratic will be 0. 6 is called a double root.
At a double root, the graph does not cross the x-axis. It just touches it.
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