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 vertex form could be

(x - 3)^2 - c    where c is the y coordinate of the vertex This graph would open upwards.  The graph is symmetrical about the line x = 3

-  so if  it has 2 distinct roots  they will be at equal intervals either side of x = 3 .

So we could make those root x = 1 and x = 5

f(x)  =  (x - 1 ) x - 5)  would be  an example of  what you require

f(x)   = (x - 8)(x + 2)  

16 is the absolute value

step-by-step explanation:

do it yourself this is easy

step-by-step explanation: