Interpreting Quadratic Functions in Factored Form

To match the given function with its graph, we will find its zeros. To do so, we will rewrite it a little bit. $$\begin{array}{c}y=\frac{2}{5}x(x+5)\iff y=\frac{2}{5}(x-0)(x-(\text{-}5))\end{array}$$ Note that now the quadratic function is written in factored form. $$\begin{array}{rl}\text{Factored form:}& y=a(x-p)(x-q)\\ \text{Given equation:}& y=\frac{2}{5}(x-0)(x-(\text{-}5))\end{array}$$ In this form, the zeros of the function are $p$ and $q.$ Therefore, the zeros of the given function are $0$ and $\text{-}5.$ This matches choice IV.