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

Step-by-step explanation:

For a quadratic function to have a vertex with an x-coordinate of 3, then

Let a=1, then we have

So now our equation becomes:

We now find two factors of c that add up to -6.

Let these factors be 1, and c.

Then

Therefore the factors are :

1 and -7.

The function becomes:

The factored form is