Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two distinct roots.

The definition of quadratic function is given by:



So the problem asks for two conditions:

1. Write the quadratic function in factored form.
2. The vertex has an x-coordinate of 3.

Then the equation (1) must be written as follows:



To satisfy the two conditions:



So we are free to choose the value of one root, say:



Thus:



Finally, the answer is:



The graph of this function is shown in the figure below.

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