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

The quadratic function is  f(x) = (x − 2) (x − 4)

Step-by-step explanation:

Given a vertex with an x-coordinate of 3. we have to write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two distinct roots.

As the vertex lies on the axis of symmetry, so the axis of symmetry is x = 3. Now we have to take two x-intercepts that are equal distance from the axis of symmetry i.e from point of vertex and we can use these x-intercepts to write factors of the function by subtracting from x.

we take 2 and 4 ∴ factors becomes (x-2) and (x-4)

Hence, the quadratic function is

f(x) = (x − 2) (x − 4)