Family of Polynomial Functions

A family of functions are a set of functions with the same x-intercept but different y-intercepts (unless zero is a y-intercept). In general, a family of functions will have the format \(y = k(x - a_1)(x - a_2)(x - a_3)\ldots (x - a_n) \text{ where } k\epsilon\mathbb{R}, k\neq0\)

Questions will typically ask to find a member of a specific function family by stating the roots and giving a point. The point can be used to find the value of \(k\) by subbing in x and y.