Interpreting Quadratic Functions in Factored Form

We are told that the graph passes through $(0,0)$ and $(6,0).$ Since the $y\text{-}$coordinate of these points is $0,$ we know that $0$ and $6$ are the $x\text{-}$intercepts. We can partially write a quadratic function in factored form using this information. $$\begin{array}{c}y=a(x-0)(x-6)\iff y=ax(x-6)\end{array}$$ Since the value of $a$ does not affect the zeros, we can choose any value. For simplicity, we will choose $a=1.$ $$\begin{array}{c}y=1x(x-6)\iff y=x(x-6)\end{array}$$