How to get from vertex to factored form?

Foil the factored form, to make a polynomial ax^2 + bx + c,Usually the vertex comes from a polynomial. Then you find the x of the vertex and use this equation : () now you have h or the x and plug in h to: a(x-h)^2+k = y. y being the y intercept to find that you plug in your x intercepts into the polynomial, and using algebra you get k=y-a(x-h)^2. Now you have your vertex:(h,k)