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

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5