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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