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 vertex lies on the axis of symmetry so the axis of symmetry is x = 3. Find any two intercepts that are equal distance from the axis of symmetry. Use those intercepts to write factors of the function by subtracting their values from x. For example, 2 and 4 are each 1 unit from x = 3 so f (x) = (x - 2) (x - 4) is a possible function. Trust me this is the answer