\[ f(x)=-(x+1)^{2}(x-2)^{2} \] Answer the questions regarding the graph of \( f \). hen, use this information to graph the function (a) Choose the end behavior of the graph of \( f \). Choose One

As \( x \) approaches negative infinity, \( f(x) \) also approaches negative infinity; conversely, as \( x \) approaches positive infinity, \( f(x) \) heads towards negative infinity as well. This indicates that the graph of \( f(x) \) will drop down on both ends, typical of a function with a negative leading coefficient and an even degree. The function is a polynomial with even multiplicities at its critical points, which leads to a graph that touches the x-axis at the roots without crossing it. The roots of the function \( f(x) \) occur at \( x = -1 \) and \( x = 2 \), and understanding these characteristics will help illustrate how the function behaves around these points as you sketch the graph.